diff --git "a/JdE0T4oBgHgl3EQfSACX/content/tmp_files/load_file.txt" "b/JdE0T4oBgHgl3EQfSACX/content/tmp_files/load_file.txt" new file mode 100644--- /dev/null +++ "b/JdE0T4oBgHgl3EQfSACX/content/tmp_files/load_file.txt" @@ -0,0 +1,1549 @@ +filepath=/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf,len=1548 +page_content='arXiv:2301.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content='02216v1 [gr-qc] 5 Jan 2023 Logarithm Corrections and Thermodynamics for Horndeski gravity like Black Holes Riasat Ali,1, ∗ Zunaira Akhtar,2, † Rimsha Babar,3, ‡ G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content=' Mustafa,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content='4,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content=' § and Xia Tiecheng1,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content=' ¶ 1Department of Mathematics,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content=' Shanghai University,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content=' Shanghai-200444,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content=' Shanghai,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content=' People’s Republic of China 2Department of Mathematics,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content=' University of the Punjab,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content=' Quaid-e-Azam Campus,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content=' Lahore 54590,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content=' Pakistan 3Division of Science and Technology,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content=' University of Education,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content=' Township,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content=' Lahore-54590,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content=' Pakistan 4Department of Physics Zhejiang Normal University Jinhua 321004,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content=' People’s Republic of China In this paper,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content=' we compute the Hawking temperature by applying quantum tunneling approach for the Horndeski like black holes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content=' We utilize the semi-classical phenomenon and WKB approximation to the Lagrangian field equation involving generalized uncertainty principle (GUP) and compute the tunneling rate as well as Hawking temperature.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content=' For the zero gravity parameter, we obtain results consistent without correction parameter or original tunneling.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content=' Moreover, we study the thermal fluctuations of the considered geometry and examine the stable state of the system by heat capacity technique.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content=' We also investigate the behaviour of thermodynamic quantities under the influence of thermal fluctuations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content=' We observe from the graphical analysis, the corresponding system is thermodynamically stable with these correction terms.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content=' keywords: Horndeski like black holes;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content=' Quantum gravity;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content=' Tunneling radiation, Thermal fluctuations, Corrected entropy, Phase transition.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content=' I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content=' INTRODUCTION Tunneling is the semi-classical mechanism in which particles have radiated from black hole (BH) outer horizon.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content=' Some analysis shows the keen interest in the Hawking temperature (TH) via tunneling method from different BHs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content=' The main aspect to examine the TH is the imaginary part of classical action which leads to the tunneling radiation of boson particles appearing from the Horndeski like BHs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content=' The quantum tunneling and TH of charged fermions in BHs has been observed [1].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content=' In this paper, they examined that the tunneling and TH depend on charges of electric and magnetic, acceleration, rotation, mass and NUT parameter of the charged pair BHs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content=' The tunneling strategy from Reissner Nordstom-de Sitter BH like solution in global monopole has been analyzed [2].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content=' In this article, the authors observed that the modified TH depends on the parameter of global monopole.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content=' The BH thermodynamics have been examined [3] with some parameters like acceleration, NUT and rotation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content=' The researchers studied thermodynamical quantities like the area, entropy, surface gravity and TH.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content=' The tunneling spectrum of bosonic particles has been computed from the modified BHs horizon by utilizing the Proca field equation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content=' Hawking evaluated tunneling probability from BH [4] by utilizing theoretical technique and later, it has been explained by Parikh and Wilczek [5, 6].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content=' The important of this radiation represents that vacuum thermal fluctuation produce pairs of particle (particle and anti-particle) from the horizon.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content=' Hawking considered that the particle’s have ability to emit from the BH and the anti-particles have no ability to radiate from the horizon.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content=' Parikh and Wilczek explained a mathematical approach by utilizing WKB approximation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content=' This phenomenon use geometrical optic approximation which is another view of eikonal approximation in wave clarification [7].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content=' The set of all particles remain at the front boundary and with the emission of these particles, the BH mass reduces in the form of particles energy.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content=' In the Parikh-Wilczek method, a precisely tunneling was established and there were as still unanswered problems like information release, temperature unitary and divergence.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content=' Many authors have made efforts on the tunneling strategy and semi-classical phenomenon from the different BHs horizon;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content=' one of the important explanations can be checked in [8]-[31].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content=' The radiate particles for many BHs have been analyzed and also computed the radiate particles with the influences of the geometry of BH with different parameters.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content=' It is possible to study modified thermodynamic properties of BH by considering generalized uncertainty principle (GUP) influences [32].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content=' The GUP implies high energy ∗Electronic address: riasatyasin@gmail.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content='com †Electronic address: zunaira.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content='math.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content='pu@gmail.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content='com ‡Electronic address: rimsha.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content='babar10@gmail.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content='com §Electronic address: gmustafa3828@gmail.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content='com ¶Electronic address: xiatc@shu.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content='edu.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content='cn 2 result to thermodynamic of BH, by considering the quantum gravity theory with a minimal length.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content=' By considering the GUP influences, it is viable to examine the modified thermodynamic of BHs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content=' It is a well known fact that thermal fluctuations are a result of statistical perturbations in the dense matter.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content=' With the emission of Hawking radiations from the BH, the size of BH reduces and consequently its temperature increases.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content=' Faizal and his colleague [33] have studied the thermodynamics and thermal fluctuations of generalized Schwarschild BH, (i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content=', Reissner-Nordstrom, Kerr and charged AdS BHs) with the help first-order corrections and discussed the stability of BHs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content=' The thermodynamics of rotating Kerr-AdS BH and its phase transition have been studied by Pourhassan and Faizal [34].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content=' They concluded that the entropy corrections are very helpful to examine the geometry of small BHs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content=' By applying the stability test of heat capacity and Hessian matrix, the phase transition as well as thermodynamics of non-minimal regular BHs in the presence of cosmological constant has been investigated [35] and the authors concluded that the local and global stability of the corresponding BHs increases for higher values of correction parameters.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content=' Zhang and Pradhan [36, 37] have investigated the corrected entropy and second order phase transition via thermal fluctuations on the charged accelerating BHs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content=' Moreover, the thermodynamics and geometrical analysis of new Schwarzschild BHs have been studied [38, 39].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content=' By using the tunneling approach under the influence of quantum gravity the Hawking temperture for different types of BH have been discussed [40]-[44].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content=' Sharif and Zunaira [45, 46] have computed the thermodynamics, quasi-normal modeand thermal fluctuations of charged BHs with the help of Weyl corrections.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content=' The authors found that the system is unstable for the small radii of BHs under the influence of first order corrections and by using the heat capacity and Hessian matrix technique, they have also studied the stable conditions of the system.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content=' The authors in [47, 48] have investigated the thermodynamics, phase transition and local/global stability of NUT BH via charged, accelerating as well as rotating pairs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content=' Ilyas et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content=' [49–52] discussed the energy conditions and calculated the new solutions for stellar structures by taking black hole geometry as exterior spacetime in the background of different modified theories of gravity.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content=' Recently, Ditta et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content=' [53] discussed the thermal stability and Joule–Thomson expansion of regular BTZ-like black hole.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content=' The main intention of this paper is to investigate the tunneling radiation without self-gravity and back-reaction and also explain the modified tunneling rate.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content=' The tunneling radiation is evaluated under the conditions of charge-energy conservation, Horndeski parameter and GUP parameter influences.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content=' The modified TH depends on the Horndeski parameter as well as GUP parameter and also investigated the behaviour of thermodynamic quantities via thermal fluctuations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content=' This paper is based on the analysis of quantum tunneling, TH, stability and instability conditions for the Horndeski like BH.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content=' The paper is outlined as follows: in Sec.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content=' II, we study the tunneling radiation of bosonic particles for 4D Horndeski like BH and also calculate the effects of GUP parameters on tunneling and TH.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content=' In section III, we study the graphical presentation of tunneling radiation for this type of BH and analyze the stable and unstable conditions for Horndeski like BH.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content=' In section IV, we investigate the behaviour of thermodynamic quantities under the effects of thermal fluctuations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content=' In section V, we express the discussion and conclusion of the whole analysis.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content=' II.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content=' HORNDESKI LIKE BLACK HOLES Hui and his coauthor Nicolis [58] argued that the no-hair theorems cannot be applied on a Galileon field, as it is coupled to gravity under the effect of peculiar derivative interactions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content=' Further, they demonstrated that static and spherically symmetric spacetime defining the geometry of the black hole could not sustain nontrivial Galileon profiles.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content=' Babichev and Charmousis [59] examined the no-hair theorem in Ref.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content=' [58] by considering Horndeski theories and beyond.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content=' Furthermore, they provided the Lagrangian of Horndeski theory which can be expressed as a generalized Galileon Lagrangian, which is defined as S = � √−g � Q2(χ) + Q3(χ)□φ + Q4(χ)R + Q4,χ � (□φ)2�� .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content=' − (∇ǫ∇εφ) (∇ǫ∇εφ)] + Q5(χ)Gǫε∇ǫ∇εφ − 1 6Q5,χ � (□φ)3 − 3(□φ) (∇ǫ∇vφ) (∇ǫ∇εφ) +2 (∇ǫ∇εφ) (∇v∇γφ) (∇γ∇ǫφ)]} d4x.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content=' (1) where Q2, Q3, Q4, and Q5 are the arbitrary functions of the scalar field φ and χ = −∂ǫφ∂ǫφ/2 represents the canonical kinetic term.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content=' Additionally, in the current analysis, fχ stands for ∂f(χ)/∂χ, Gǫε is the Einstein tensorR is the Ricci scalar, and other relations are defined as: (∇ǫ∇εφ)2 ≡ ∇ǫ∇εφ∇ε∇ǫφ (∇ǫ∇εφ)3 ≡ ∇ǫ∇εφ∇ε∇ρφ∇ρ∇ǫφ (2) 3 The scalar field admits the Galilean shift symmetry ∂ǫφ → ∂ǫφ + bǫ in flat spacetime for Q2 ∼ Q3 ∼ χ and Q4 ∼ Q5 ∼ χ2, which resembles the Galilean symmetry [60].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content=' In the current study, we investigate the tunneling radiation of spin-1 massive boson particles from Horndeski-like BH.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content=' For this purpose, we adopted the procedure, which is already reported in [57] for Horndeski spacetime.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content=' Finally, we have the following spacetime: ds2 = − � 1 − 2rM(r) Σ � dt2 + 1 ∇(r)Σdr2 + Σ2dθ2 − A Σ sin2 dφ2 − 4ar Σ M(r) sin2 θdtdφ, (3) with Σ2 = a2 cos2 θ + r2 and ∇(r) = a2 − 2rM(r)+ r2, M(r) = M − 1 2QIn r r0 and A = (a2 + r2)2 − ∇a2 sin2 θ, while a, Q and M represent the rotation parameter, Horndeski parameter and mass of BH, respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content=' If Q → 0, the metric (3) goes over to the Kerr BH [61] and if Q = a = 0 the metric (3) also goes over to the Schwarzschild metric.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content=' The line-element (3) can be re-written as ds2 = −f(r)dt2 + g−1(r)dr2 + I(r)dφ2 + h(r)dθ2 + 2R(r)dtdφ (4) where f(r) = � 1 − 2rM(r) Σ � , g−1(r) = 1 ∇Σ, h(r) = Σ2, I(r) = −A Σ sin2, R(r) = −2ar Σ M(r) sin2 θ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content=' We study the tunneling radiation of spin-1 particles from four-dimensional Horndeski like BHs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content=' By utilizing the Hamilton-Jacobi ansatz and the WKB approximation to the modified field equation for the Horndeski space-time, the tunneling phenomenon is successfully applied.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content=' We study the modified filed equation on a four dimensional space-time with the background of rotation parameter, Horndeski parameter and evaluated for the radial function.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content=' As a result, we get the tunneling probability of the radiated particles and derive the modified TH of Horndeski like BHs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content=' The modified filed equation is expressed by [27,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content=' 30] ∂µ �√−gΨνµ� + √−g m2 ℏ2 Ψν + √−g i ℏAµΨνµ + √−g i ℏeF νµΨµ + ℏ2β∂0∂0∂0 �√−gg00Ψ0ν� −ℏ2β∂i∂i∂i �√−ggiiΨiν� = 0,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content=' (5) here Ψνµ,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content=' m and g present the anti-symmetric tensor,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content=' bosonic particle mass and determinant of coefficient matrix,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content=' so Ψνµ = � 1 − ℏ2β∂2 ν � ∂νΨµ − � 1 − ℏ2β∂2 µ � ∂µΨν + � 1 − ℏ2β∂2 ν � i ℏeAνΨµ − � 1 − ℏ2β∂2 ν � i ℏeAµΨν,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content=' and Fνµ = ∇νAµ − ∇µAν,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content=' with β,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content=' e ,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content=' ∇µ and Aµ are the GUP parameter(quantum gravity),' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content=' bosonic particle charge,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content=' covariant derivative and BH potential,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content=' respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content=' The Ψνµ can be computed as Ψ0 = −IΨ0 + RΨ3 fI + R2 , Ψ1 = 1 g−1 Ψ1, Ψ2 = 1 hΨ2, Ψ3 = RΨ0 + fΨ3 fI + R2 , Ψ01 = ˜ −DΨ01 + RΨ13 (R2 + fI)g−1 , Ψ02 = ˜ −DΨ02 (R2 + fI)h, Ψ03 = (f 2 − fI)Ψ03 (fI + R2)2 , Ψ12 = 1 g−1hΨ12, Ψ13 = 1 g−1(fI + R2)Ψ13, Ψ23 = fΨ23 + RΨ02 (fI + R2)h .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content=' In order to observe the bosonic tunneling, we have assumed Lagrangian gravity equation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content=' Further, we utilized the WKB approximation to the Lagrangian gravity equation and computed set of equations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content=' Furthermore, we have utilized the variable separation action to get required solutions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content=' The approximation of WKB is defined [?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content=' ] as Ψν = ην exp � i ℏK0(t, r, φ, θ) + ΣℏnKn(t, r, φ, θ) � .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content=' (6) we get set of equations in Appendix A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content=' Utilizing variable separation technique, we can take K0 = −(E − Lω)t + W(r) + Lφ + ν(θ), (7) 4 where E and L present the particle energy and particle angular, respectively, corresponding to angle φ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content=' After considering Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content=' (7) into Eqs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content=' (22)-(25),' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content=' we reach a matrix in the form U(η0,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content=' η1,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content=' η2,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content=' η3)T = 0,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content=' which express a 4 × 4 matrix presented as ”U”,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content=' whose elements are given as follows: U00 = −I g−1(fI + R2) � W 2 1 + βW 4 1 � − I (fI + R2)h � L2 + βL4� − fI (fI + R2)2 � ν2 1 + βν4 1 � − m2I (fI + R2),' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content=' U01 = −I g−1(fI + R2) � ((E − Lω) + (E − Lω)3β + A0e + (E − Lω)2βeA0 � W1 + R g−1(fI + R2) + � ν1 + βν3 1 � ,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content=' U02 = −I h(fI + R2) � (E − Lω) + (E − Lω)3β − A0e − (E − Lω)2βeA0 � L,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content=' U03 = −R g−1(fI + R2) � W 2 1 + βW 4 1 � − fI h(fI + R2)2 � (E − Lω)3β − (E − Lω)2βeA0 + (E − Lω) − eA0 � ν1 + m2R (fI + R2)2 ,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content=' U12 = 1 g−1h � W1 + βW 3 1 � L,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content=' U11 = −I g−1(fI + R2) � β(E − Lω)4 − βeA0EW 2 1 + (E − Lω)2 − eA0(E − Lω) � + R (fI + R2)g−1 + � ν1 + βν3 1 � (E − Lω) − 1 g−1h � L2 + βL4� − 1 (fI + R2)g−1 � ν1 + βν3 1 � − m2 g−1 − eA0I (fI + R2)g−1 × � (E − Lω) + (E − Lω)3β − A0e − (E − Lω)2βeA0 � + eA0R g−1(fI + R2) � ν1 + βν3 1 � ,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content=' U13 = −R g−1(fI + R2) � W1 + βW 3 1 � (E − Lω) + 1 g−1(fI + R2)2 � W1 + βW 3 1 � ν1 + ReA0 g−1(fI + R2) � W1 + βW 3 1 � ,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content=' U20 = I h(fI + R2) � (E − Lω)L + β(E − Lω)L3� + R h(fI + R2) � (E − Lω) + β(E − Lω)3ν2 1 � − IeA0 h(fI + R2) � L + βL3� ,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content=' U22 = I h(R2 + fI) � βE4 − βeA0E + E2 − eA0(E − Lω) � − 1 g−1h + R h(R2 + fI) � (E − Lω)3β + −(E − Lω)2βeA0 − A0e + (E − Lω) � ν1 − f h(R2 + fI) � ν2 1 + βν4 1 � − m2 h − eA0I h(fI + R2) � (E − Lω) + (E − Lω)3β − A0e − (E − Lω)2βeA0 � ,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content=' U23 = f h(fI + R2) � L + βL3� ν1,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content=' U30 = (fI − f 2) (fI + R2)2 � ν1 + βν3 1 � E + R h(fI + R2) � L2 + βL4� − m2R (fI + R2) − eA0(fI − f 2) (fI + R2)2 � ν1 + βν3 1 � ,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content=' U31 = 1 g−1(fI + R2) � ν1 + βν3 1 � W1,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content=' U32 = R h(R2 + fI) � L + βL3� E + f h(R2 + fI) � ν1 + βν3 1 � L,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content=' U33 = (fI − f 2) (fI + R2) � (E − Lω)2 − eA0(E − Lω) + β(E − Lω)4 − βeA0(E − Lω)3� − 1 g−1(R2 + fI) � W 2 1 + βW 4 1 � − f (R2 + fI)h � L2 + βL4� − m2f (fI + R2) − eA0(fI − f 2) (fI + R2) × � (E − Lω) + β(E − Lω)3 − eA0(E ��� Lω)2� ,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content=' 5 with ∂tK0 = (E − Lω),' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content=' ∂φK0 = L,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content=' W1 = ∂rK0 and ν1 = ∂θK0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content=' For non-trivial solution, we get ImW ± = ± � � � � � � E − LΩ − eA0 �2 + Z1 � 1 + β Z2 Z1 � (fI + R2)gI−1 dr, = ±iπ � R − LΩ − A0e � + � 1 + βA � 2k(r+) , (8) where Z1 = (E − Lω)ν1 g−1R fI + R2 + fg−1 fI + R2 ν2 1 − g−1m2, Z2 = g−1I fI + R2 � (R − LΩ)4 + (eA0)2(R − LΩ)2 − 2A0e(R − LΩ)3� + g−1R h(fI + R2) � (R − LΩ)3 − eA0(R − LΩ)2� ν1 − fg−1 fI + R2 ν4 1 − W 4 1 .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content=' and A is a arbitrary parameter.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content=' In particular case, we take the radial component of the action of particle, for this aim we choose a components of matrix equals to zero.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content=' Since, we have found the tunneling radiation (related to Horndeski gravity and quantum gravity) for BH.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content=' This tunneling and TH quantities relate on the Horndeski gravity and quantum gravity of this particular physical object.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content=' Thus, we have found the corresponding TH which important as a component of leading metric with Horndeski gravity and quantum gravity.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content=' Such that, in this method we are not concerned in order of higher for Planck’s constant only obtained appropriate result.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content=' The generalized tunneling depends on the BHs metric and Horndeski gravity and GUP parameter.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content=' The generalized tunneling for Horndeski like BH can be written as T = Temission Tabsorption = exp � −2π(R − LΩ − A0e) k(r+) � [1 + βA] , (9) with k(r+) = 4πr+ � a2 + r2 + � Qr+ + −a2 + r2 + (10) In the presence of GUP terms, we calculate the TH of the Horndeski gravity BHs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content=' by taking the Boltzmann factor TB = exp [(E − Lω − eA0)/TH] as TH = −a2 + Qr+ + r2 + 4πr+ � a2 + r2 + � [1 − βA] .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content=' (11) The above result shows that the TH depends on the Horndeski gravity, GUP parameter, rotation parameter, Horndeski gravity, arbitrary parameter A and radius (r+) of BH.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content=' When β = 0, we obtain the general TH in [57].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content=' In the absence of charge i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content=', Q = 0, the above temperature reduces into Kerr BH temperature [58, 59].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content=' For β = 0 and a = 0, the temperature reduces into Reissner Nordstr¨om BH.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content=' Moreover, when Q = 0 = a, we recover the temperature of Schwarzschild BH [60].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content=' The quantum corrections slow down the increase in TH throughout the radiation phenomenon.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content=' TH versus r+ We observe the geometrical presentation of TH w.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content='r.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content='t r+ for the 4D Horndeski like metric.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content=' Moreover, we observe the physical significance of these graphs under Horndeski gravity and GUP parameter and study the stability and instability analysis of corresponding TH.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content=' For β equals to zero, the tunneling radiation will be independent of GUP parameter.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content=' In the left plot of Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content=' 1, the TH increases with increasing β in small region of horizon 0 ≤ r+ ≤ 5, that indicates the stable state of BH till r+ → ∞.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content=' In the right plot of Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content=' 1, the rotating parameter and β are fixed, then we take changing values of hairy parameter of Horndeski gravity and get the completely unstable form of BH with negative temperature.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content=' 6 β=10 β=20 β=30 0 1 2 3 4 5 0 1 2 3 4 5 6 r+ TH Q=0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content='5 Q=1 Q=1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content='5 0 1 2 3 4 5 6 4 2 0 2 r+ TH Figure 1: TH w.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content='r.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content='t horizon r+ for a = 5, Q = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content='5 and Ξ = 1 and left β = 10 (black), β = 20 (blue), β = 30 (red).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content=' Right a = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content='5, Ξ = 1, β = 5, Q = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content='5 (black), a = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content='5, Ξ = 1, β = 5, Q = 1 (blue), a = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content='5, Ξ = 1, β = 5, Q = 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content='5 (red).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content=' III.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content=' THERMODYNAMICS AND EFFECTS OF FIRST ORDER CORRECTIONS Thermal fluctuations plays important role on the study of BH thermodynamics.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content=' With the concept of Euclidean quantum gravity, the temporal coordinates shifts towards complex plan.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content=' To check the effects of these correction in entropy, we find Hawking temperature and usual entropy of the given system with the help of first law of thermody- namics S = π � a2 + r2 + � , T = −a2 + Qr+ + r2 + 4πr+ � a2 + r2 + � (12) To check the corrected entropy along these thermal fluctuations, the partition function is Z(µ) in terms of density of states η(E) is given as [37] Z(µ) = � ∞ 0 exp(−µE)η(E)dE, (13) where T+ = 1 µ and E is the mean energy of thermal radiations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content=' By using the Laplace inverse transform, the expression of density takes the form ρ(E) = 1 2πi � µ0+i∞ µ0−i∞ Z(µ) exp(µE)dµ = 1 2πi � µ0+i∞ µ0−i∞ exp( ˜S(µ))dµ, (14) where ˜S(µ) = µE + ln Z(µ) represents the modified entropy of the considered system that is dependent on Hawking temperature.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content=' Moreover, the expression of entropy gets modified with the help of steepest decent method, ˜S(µ) = S + 1 2(µ − µ0)2 ∂2 ˜S(µ) ∂µ2 ��� µ=µ0 + higher-order terms.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content=' (15) Using the conditions ∂ ˜S ∂µ = 0 and ∂2 ˜S ∂µ2 > 0, the corrected entropy relation under the first-order corrections modified.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content=' By neglecting higher order terms, the exact expression of entropy is expressed as ˜S = S − δ ln(ST 2), (16) where δ is called correction parameter, the usual entropy of considered system is attained by fixing δ = 0 that is without influence of these corrections.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content=' Furthermore, inserting the Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content=' (12) into (16), we have ˜S = (a2 + r2 +) − δ log �� a2 − r+ (Q + r+) �2 16πr2 + � a2 + r2 + � � .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content=' (17) 7 δ=0 δ=0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content='4 δ=0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content='6 δ=0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content='6 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content='0 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content='1 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content='2 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content='3 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content='4 10 20 30 40 r+ S ˜ Figure 2: Corrected entropy versus r+ for a=0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content='2, Q=0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content='4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content=' In the Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content=' 2, the graph of corrected entropy is monotonically increasing throughout the considered domain.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content=' It is noted the graph (black) of usual entropy is increasing just for small value of horizon radius but corrected expression of energy is increasing smoothly.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content=' Thus, these corrections terms are more effective for small BHs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content=' Now, using the expression of corrected entropy and check the other other thermodynamic quantities via thermal fluctuations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content=' In this way, the the Helmholtz energy (F = − � ˜SdT ) leads to the form F = � a4 − r2 + � −4a2 + 2Qr+ + r2 + �� � δ log � (a2−r+(Q+r+)) 2 { r2 + � a2 + r2 + � } � − a2 − δ log(16π) − r2 + � 4πr2 + � a2 + r2 + �2 .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content=' (18) δ=0 δ=0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content='4 δ=0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content='6 δ=0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content='6 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content='00 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content='05 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content='10 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content='15 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content='20 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content='25 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content='30 35 40 45 50 55 60 65 r+ F Figure 3: Helmholtz free energy versus r+ for a=0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content='2, Q=0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content='4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content='. The Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content=' 3 shows the graph of Helmholtz free energy versus horizon radius.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content=' It is observed that the behaviour of energy is gradually decreases for the different correction parameter δ values.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content=' While the graph of usual entropy shows opposite behaviour as the graph is increasing.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content=' This behaviour means, the considered system shifts its state towards equilibrium, thus, no more work can be extract from it.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content=' The expression of internal energy (E = F + T ˜S) for the corresponding geometry is given by [37] E = � r+ � a2 + r2 + � � r+ (Q + r+) − a2� � δ � log(16π) − log �� a2 − r+ (Q + r+) � 2 r2 + � a2 + r2 + � �� + π � a2 + r2 + � � − � a4 − r2 + � −4a2 + 2Qr+ + r2 + �� � −δ log �� a2 − r+ (Q + r+) �2 r2 + � a2 + r2 + � � + a2 + δ log(16π) + r2 + � � � 4πr2 + � a2 + r2 + �2 �−1 .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content=' (19) 8 δ=0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content='2 δ=0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content='4 δ=0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content='6 δ=0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content='8 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content='0 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content='1 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content='2 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content='3 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content='4 2 0 2 4 6 r+ E Figure 4: Internal Energy w.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content='r.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content='t r+ for a=0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content='2, Q=0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content='4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content=' The graphical behaviour of internal energy for the different choices of horizon radius is shown in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content=' 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content=' It is observable that for the small values of radii, the graph is gradually decreases even shifts towards negative side, While the corrected internal energy depicts positive behaviour.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content=' This mean that the considered BH absorbing more and more heat from the surrounding to maintain its state.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content=' Since, BHs considered as a thermodynamic system, so there is another important thermodynamic quantity that is pressure.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content=' In this regard, there is deep connection between voulme (V = 2π(r2 ++a2)(2r2 ++a2) 3r+ ) and pressure.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content=' The Expression of BH pressure (P = − dF ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content='dV ) under the effect of thermal ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content='fluctuations takes the form ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content='P = ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content='� ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content='2r2 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content='+ ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content='� ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content='a2 + r2 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content='+ ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content='�� ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content='− 4a2 + 3Qr+ + 2r2 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content='+ ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content='�� ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content='a2 − r+ ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content='� ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content='Q + r+ ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content='��2� ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content='− δ log ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content='��� ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content='a2 − r+(Q + r+) ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content='�2� ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content='(r2 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content='+(a2 + r2 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content='+))−1� ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content='+ a2 + δ log(16π) + r2 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content='+ ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content='� ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content='− 2 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content='� ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content='r+ ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content='� ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content='Q + r+ ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content='� ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content='− a2�� ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content='a4 − r2 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content='+ ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content='� ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content='− 4a2 + 2Qr+ + r2 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content='+ ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content='��� ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content='− a4δ + Qr3 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content='+ ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content='� ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content='a2 + δ ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content='� ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content='− r2 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content='+ ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content='� ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content='a4 + 3a2δ ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content='� ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content='+ Qr5 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content='+ + r6 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content='+ ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content='� ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content='+ 4r2 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content='+ ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content='� ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content='a4 − r2 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content='+ ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content='� ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content='− 4a2 + 2Qr+ + r2 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content='+ ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content='��� ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content='a2 − r+ ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content='� ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content='Q + r+ ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content='��2� ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content='− δ log ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content='× ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content='��� ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content='a2 − r+ ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content='� ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content='Q + r+ ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content='��2�� ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content='r2 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content='+ ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content='� ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content='a2 + r2 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content='+ ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content='��−1� ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content='+ a2 + δ log(16π) + r2 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content='+ ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content='� ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content='+ 2 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content='� ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content='a2 + r2 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content='+ ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content='�� ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content='a4 − r2 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content='+ ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content='� ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content='− 4a2 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content='+ 2Qr+ + r2 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content='+ ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content='��� ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content='a2 − r+ ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content='� ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content='Q + r+ ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content='��2� ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content='− δ log ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content='��� ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content='a2 − r+ ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content='� ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content='Q + r+ ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content='��2� ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content='(r2 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content='+ ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content='� ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content='a2 + r2 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content='+ ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content='��−1� ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content='+ a2 + δ log(16π) ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content='+ r2 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content='+ ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content='��� ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content='4πr3 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content='+ ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content='� ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content='a2 + r2 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content='+ ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content='�3� ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content='a2 − r+ ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content='� ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content='Q + r+ ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content='��2�−1 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content='.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content=' (20) δ=0 δ=0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content='2 δ=0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content='4 δ=0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content='6 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content='0 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content='5 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content='0 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content='5 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content='0 0 1 ×108 2 �108 3 �108 4 �108 5 �108 r+ P Figure 5: Pressure versus r+ for a=0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content='2, Q=0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content='4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content=' In the Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content=' 5, the graph of pressure is just coincides the state of equilibrium.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content=' For the different values of correction parameter, the pressure is significantly increases for the considered system.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content=' Further, there is another important thermodynamic quantity enthalpy (H = E + PV ) is given in Appendix B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content=' 9 δ=0 δ=0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content='4 δ=0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content='6 δ=0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content='8 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content='0 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content='2 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content='4 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content='6 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content='8 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content='0 10 5 0 5 r+ H Figure 6: Enthalpy versus r+ for a=0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content='2, Q=0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content='4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content=' From Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content=' 6, it can observed that the graph of usual enthalpy is coincide with the plots of corrected one and abruptly decreases even shifts towards negative side.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content=' This means that there exists a exothermic reactions means there will be huge amount of energy release into its surroundings.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content=' By taking into account the thermal fluctuations, the Gibbs free energy (G = H − T ˜S) is expressed in Appendix B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content=' δ=0 δ=0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content='4 δ=0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content='6 δ=0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content='8 0 5 10 15 20 5 10 15 20 r+ G Figure 7: Gibbs free energy versus r+ for a=0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content='2, Q=0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content='4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content=' The graphical analysis of Gibbs free energy with respect to horizon radius is shows in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content=' 7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content=' The positivity of this energy is sign of occurrence of non-spontaneous reactions means this system requires more energy to gain equilibrium state.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content=' After the detail discussion of thermodynamics quantities, there is another important concept is the stability of the system that is checked by specific heat.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content=' The specific heat (C ˜S = dE ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content='dT ) is given as ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content='C ˜S = ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content='� ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content='2 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content='� ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content='a2 + 3r2 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content='+ ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content='�� ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content='r+ ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content='� ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content='r+ ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content='� ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content='a2� ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content='− δ(Q − 4) log ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content='� ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content='� ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content='a2 − r+ ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content='� ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content='Q + r+ ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content='��2 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content='r2 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content='+ ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content='� ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content='a2 + r2 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content='+ ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content='� ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content='� ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content='+ a2(πQ − 5) + δ(Q − 4) log(16π) ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content='� ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content='+ r+ ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content='+ ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content='� ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content='− πa4 − 2δQ log ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content='� ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content='� ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content='a2 − r+ ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content='� ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content='Q + r+ ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content='��2 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content='r2 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content='+ ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content='� ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content='a2 + r2 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content='+ ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content='� ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content='� ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content='+ r+ ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content='� ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content='− δ(Q + 1) log ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content='� ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content='� ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content='a2 − r+ ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content='� ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content='Q + r+ ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content='��2 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content='r2 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content='+ ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content='� ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content='a2 + r2 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content='+ ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content='� ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content='� ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content='+ r+ ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content='� ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content='− δ log ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content='× ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content='� ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content='� ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content='a2 − r+ ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content='� ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content='Q + r+ ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content='��2 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content='r2 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content='+ ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content='� ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content='a2 + r2 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content='+ ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content='� ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content='� ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content='+ πa2 + δ log(16π) + r+ ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content='� ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content='πQ + πr+ + 1 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content='� ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content='+ 2Q ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content='� ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content='+ a2(2πQ − 3) + δ(Q + 1) log(16π) ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content='� ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content='+ 2a2Q + 2δQ log(16π) ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content='�� ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content='− a4� ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content='− δ log ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content='� ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content='� ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content='a2 − r+ ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content='� ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content='Q + r+ ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content='��2 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content='r2 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content='+ ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content='� ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content='a2 + r2 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content='+ ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content='� ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content='� ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content='+ πa2 + δ log(16π) ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content='�� ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content='− a4� ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content='− δ log ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content='× ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content='� ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content='� ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content='a2 − r+ ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content='� ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content='Q + r+ ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content='��2 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content='r2 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content='+ ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content='� ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content='a2 + r2 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content='+ ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content='� ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content='� ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content='+ a2 + δ log(16π) ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content='���� ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content='r+ ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content='� ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content='a2 + r2 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content='+ ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content='���� ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content='− a4 − 4a2r2 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content='+ + 2Qr3 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content='+ + r4 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content='+ ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content='��−1 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content='.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content=' (21) 10 δ=0 δ=0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content='4 δ=0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content='6 δ=0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content='8 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content='00 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content='02 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content='04 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content='06 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content='08 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content='10 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content='10 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content='05 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content='00 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content='05 r+ CS ~ Figure 8: Specific heat versus r+ for a=0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content='2, Q=0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content='4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content=' From Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content=' 8, the behaviour of specific heat is observed with respect to horizon radius and different choices of correction parameter δ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content=' It can be observed that the uncorrected quantity (black) depicts negative behaviour means the system is unstable while the corrected specific heat shows positive behaviour throughout the considered domain.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content=' The positivity of this plot is indication of stable region.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content=' It can be concluded that these correction terms makes the system stable under thermal fluctuations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content=' IV.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content=' DISCUSSION AND RESULT In this paper, we have utilized Lagrangian gravity equation to observe the tunneling of bosonic particles through the horizon of Horndeski like BH.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content=' We have used the metric from Ref.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content=' [57].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content=' We have considered a new version of black hole with Horndeski parameter Q and a rotation parameter a, due to the presence of these parameters, we call the metric a new type of spacetime.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content=' Our results are also in terms of these parameters, therefore they are different from the previous literature related about the thermodynamics of this black hole.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content=' Assuming to relativistic quantum mechanics and the region of vacuum, where particles are produced continuously in the phenomenon of annihilated.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content=' The tunneling radiation as a quantum mechanical processes can be observed as a tunneling phenomenon, where positive boson particle radiate the horizon and the negative energy boson particle move inward and absorbed by the BH.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content=' The incoming and outgoing boson particles movement carried out by the action of particle’s is real and complex, respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content=' The emission rate of these tunneling radiation corresponding to the Horndeski like BH configuration is associated to the imaginary part of the action of particles, which is associated to the factor of Boltzmann, this factor gives TH for Horndeski like BH.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content=' From our investigation, we have observed that, in rotating case of BH, the TH at which boson particles tunnel through the BH horizon is not dependent at any types of particles.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content=' In special case when particles have different (zero or upward or down) spins, the tunneling rate will be alike by assuming the semi-classical approach.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content=' Thus, their corresponding TH must be similar for all types of particle.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content=' Therefore, one can say tunneling radiation is independent of all kinds of the particles and this result also holds for different frame of coordinates by utilizing the transformations of particular coordinate.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content=' For this procedure, the tunneling particles is associated to the energy of particles, momentum, quantum gravity, hairy parameter of Horndeski gravity and BH surface gravity, while the temperature depends on hairy parameter of Horndeski gravity, rotation and quantum gravity parameters.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content=' It is very important to mention here that, when β = 0, we obtain the standard temperature for Horndeski like BH.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content=' In the absence of charge i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content=', Q = 0, the above temperature reduces into Kerr BH temperature.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content=' For β = 0 and a = 0, the temperature reduces into Reissner Nordstr¨om BH.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content=' Moreover, when Q = 0 = a, we recover the temperature of Schwarzschild BH.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content=' For the changing values of β from 10 to 30 in the region 0 ≤ r+ ≤ 5, we have observed that the Horndeski like BH is stable and for changing Q from 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content='5 to 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content='5, the Horndeski like BH is un-stable with negative temperature.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content=' Moreover, the temperature increases with the increasing values of quantum gravity β.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content=' Moreover, we have computed TH as well as heat capacity for Horndeski gravity like BHs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content=' Firstly, the TH is calculated through entropy and the density of state is also calculated with help of inverse Laplace transformation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content=' We have observed that the exact entropy of the system depends on Hawking temperature by applying the method of steepest descent under different conditions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content=' In graphically, we have studied the monotonically increasing entropy of the metric throughout the assumed domain.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content=' It is observed that a decrease in entropy for a certain value of the radius, the corrected expression of energy is increasing smoothly and also studied that the small BHs are more effective for thermal fluctuations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content=' It is observed that the behaviour of energy gradually decreases for the different correction parameter δ values and the graph of usual entropy shows opposite behaviour as the graph increases.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content=' Therefore, the considered system shifts its state towards equilibrium.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content=' It is observable that for the small values of radii, the graph gradually decreases even 11 shifts towards negative side, while the corrected internal energy depicts positive behaviour.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content=' So, the considered BH absorbed more and more heat from the surrounding to maintain its state.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content=' The graph of pressure coincides the state of equilibrium.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content=' For the different values of correction parameter, the pressure significantly increases for the considered system.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content=' It is observed that the graph of usual enthalpy coincides with the plots of corrected one and abruptly decreases even shifts towards negative side.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content=' It can be concluded that there exists a exothermic reactions means a huge amount of energy released into its surroundings.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content=' The positivity of this energy is sign of occurrence of non-spontaneous reactions means the system required more energy to gain equilibrium state.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content=' The behaviour of specific heat with respect to horizon radius and different choices of correction parameter δ has been observed.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content=' The uncorrected quantity depicts negative behaviour means the system is unstable while the corrected specific heat shows positive behaviour throughout the considered domain.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content=' The positivity of the plots for specific heat is indication of stable region.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content=' It can be concluded that these correction terms makes the system stable under thermal fluctuations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content=' Appendix A We have utilized the Lagrangian equation in the approximation of WKB to get following solutions,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content=' I (R2 + fI)g−1 � η1(∂0K0)(∂1K0) + βη1(∂0K0)3(∂1K0) − η0(∂1K0)2 − βη0(∂1K0)4 + η1eA0(∂1K0) + η1βeA0(∂0K0)2(∂1K0) � − R g−1(fI + R2) � η3(∂1K0)2 + βη3(∂1K0)4 − η1(∂1K0)(∂3K0) − βη1(∂1K0)(∂3K0)2� + I h(fI + R2) � η2(∂0K0)(∂2K0) + βη2(∂0K0)3(∂2K0) − η0(∂2K0)2 − βη0(∂2K0)4 + η2eA0(∂2K0) + η2eA0β(∂0K0)2(∂1K0) � + fI (fI + R2)2 � η3(∂0K0)(∂3K0) + βη3(∂0K0)3(∂3K0) − η0(∂3K0)2 − βη0(∂3K0)4 + η3eA0(∂3K0) + η3eA0(∂0K0)2(∂3K0) � − m2 Iη0 − Rη3 (fI + R2) = 0,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content=' ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content='(22) ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content='−I ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content='g−1(fI + R2) ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content='� ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content='η1(∂0K0)2 + βη1(∂0K0)4 − η0(∂0K0)(∂1K0) − βη0(∂0K0)(∂1K0)3 + η1eA0(∂0K0) + βη1eA0(∂0K0)3� ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content='+ ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content='R ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content='g−1(fI + R2) ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content='� ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content='η3(∂0K0)(∂1K0) + βη3(∂0K0)(∂1K0)3 − η1(∂0K0)(∂3K0) − βη1(∂0K0)(∂3K0)3� ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content='+ ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content='1 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content='g−1h [η2(∂1K0)(∂2K0) + βη2(∂1K0)(∂2K0)3 − η1(∂2K0)2 − βη1(∂2K0)4� ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content='+ ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content='1 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content='g−1(fI + R2) ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content='� ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content='η3(∂1K0)(∂3K0) + βη3(∂1K0)(∂3K0)3 − η1(∂3K0)2 − βη1(∂3K0)4� ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content='− m2η1 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content='g−1 + ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content='eA0I ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content='g−1(fI + R2) ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content='� ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content='η1(∂0K0) + βη1(∂0K0)3 − η0(∂1K0) − βη0(∂1K0)3 + eA0η1 + βη1eA0(∂0K0)2) ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content='� ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content='+ ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content='eA0R ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content='g−1(fI + R2) ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content='� ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content='η3(∂1K0) + βη3(∂1K0)3 − η1(∂3K0) − βη1(∂1K0)3� ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content='= 0,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content=' ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content='(23) ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content='12 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content='I ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content='h(fI + R2) ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content='� ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content='η2(∂0K0)2 + βη2(∂0K0)4 − η0(∂0K0)(∂2K0) − βη0(∂0K0)(∂2K0)3 + η2eA0(∂0K0) + βη2eA0(∂0K0)3� ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content='+ ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content='1 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content='g−1h ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content='� ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content='η2(∂1K0)2 + βη2(∂1K0)4 − η1(∂1K0)(∂2K0) − βη1(∂1K0)(∂2K0)3� ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content='− ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content='R ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content='h(fI + R2) ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content='� ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content='η2(∂0K0)(∂3K0) ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content='+ βη2(∂0K0)3(∂3K0) − η0(∂0K0)(∂3K0) − βη0(∂0K0)3(∂3K0) + η2eA0(∂3K0) + βη2eA0(∂3K0)3� ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content='+ ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content='f ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content='h(fI + R2) ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content='� ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content='η3(∂2K0)(∂3K0) + βη3(∂2K0)3(∂3K0) − η2(∂3K0)2 − βη2(∂3K0)4� ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content='+ ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content='eA0I ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content='h(fI + R2) ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content='� ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content='η2(∂0K0) ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content='+ βη2(∂0K0)3 − η0(∂2K0) − βη0(∂2K0)3 + η2eA0 + η2βeA0(∂0K0)2� ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content='− m2η2 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content='h ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content='= 0,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content=' ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content='(24) ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content='(fI − f 2) ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content='(fI + R2)2 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content='� ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content='η3(∂0K0)2 + βη3(∂0K0)4 − η0(∂0K0)(∂3K0) − βη0(∂0K0)(∂3K0)3 + eA0η3(∂0K0) + βη3eA0(∂0K0)3� ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content='− ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content='I ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content='h(fI + R2) ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content='� ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content='η3(∂1K0)2 + βη3(∂1K0)4 − η1(∂1K0)(∂3K0) − βη1(∂1K0)(∂3K0)3� ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content='− ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content='R ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content='h(fI + R2) ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content='� ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content='η2(∂0K0)(∂2K0) + βη2(∂0K0)3(∂2K0) − η0(∂2K0)2 + βη0(∂2K0)4 + eA0η2(∂2K0) + βη2eA0∂0K0)2(∂2K0) ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content='� ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content='− ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content='eA0f ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content='h(fI + R2) ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content='� ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content='η3(∂2K0)2 + βη3(∂2K0)4 − η2(∂2K0)(∂3K0) − βη2(∂0K0)(∂3K0)3� ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content='− m2(Rη0 − fη3 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content='(fI + R2) ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content='+eA0(fI − f 2) ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content='(fI + R2)2 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content='� ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content='η3(∂0K0) + βη3(∂0K0)3 − η0(∂3K0) − βη0(∂3K0)3 + η3eA0 + η3βeA0(∂0K0)2� ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content='= 0,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content=' ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content='(25) ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content='Appendix B ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content='The thermodynamic quantity enthalpy is given as ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content='H = ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content='� ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content='r+ ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content='� ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content='a2 + r2 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content='+ ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content='�� ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content='r+ ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content='� ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content='a2 + r2 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content='+ ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content='�� ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content='r+ ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content='� ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content='Q + r+ ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content='� ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content='− a2�� ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content='δ ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content='� ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content='log(16π) − log ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content='� ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content='� ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content='a2 − r+ ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content='� ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content='Q + r+ ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content='��2 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content='r2 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content='+ ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content='� ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content='a2 + r2 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content='+ ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content='� ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content='�� ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content='+ π ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content='� ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content='a2 + r2 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content='+ ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content='�� ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content='− ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content='� ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content='a4 − r2 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content='+ ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content='� ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content='− 4a2 + 2Qr+ + r2 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content='+ ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content='��� ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content='− δ log ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content='� ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content='� ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content='a2 − r+ ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content='� ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content='Q + r+ ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content='��2 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content='r2 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content='+ ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content='� ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content='a2 + r2 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content='+ ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content='� ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content='� ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content='+ a2 + δ log(16π) + r2 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content='+ ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content='�� ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content='+ ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content='� ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content='2r2 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content='+ ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content='� ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content='a2 + r2 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content='+ ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content='�� ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content='− 4a2 + 3Qr+ + 2r2 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content='+ ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content='�� ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content='a2 − r+ ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content='� ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content='Q + r+ ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content='��2� ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content='− δ log ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content='� ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content='� ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content='a2 − r+ ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content='� ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content='Q + r+ ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content='��2 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content='r2 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content='+ ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content='� ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content='a2 + r2 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content='+ ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content='� ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content='� ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content='+ a2 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content='+ δ log(16π) + r2 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content='+ ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content='� ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content='− 2 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content='� ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content='r+ ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content='� ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content='Q + r+ ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content='� ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content='��� a2�� ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content='a4 − r2 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content='+ ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content='� ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content='− 4a2 + 2Qr+ + r2 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content='+ ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content='��� ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content='− a4δ + Qr3 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content='+ ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content='� ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content='a2 + δ ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content='� ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content='− r2 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content='+ ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content='� ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content='a4 + 3a2δ ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content='� ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content='+ Qr5 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content='+ + r6 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content='+ ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content='� ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content='+ 4r2 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content='+ ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content='� ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content='a4 − r2 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content='+ ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content='� ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content='− 4a2 + 2Qr+ + r2 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content='+ ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content='��� ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content='a2 − r+ ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content='� ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content='Q + r+ ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content='��2� ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content='− δ log ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content='× ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content='� ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content='� ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content='a2 − r+ ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content='� ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content='Q + r+ ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content='�� ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content='2 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content='r2 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content='+ ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content='� ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content='a2 + r2 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content='+ ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content='� ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content='� ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content='+ a2 + δ log(16π) + r2 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content='+ ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content='� ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content='+ 2 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content='� ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content='a2 + r2 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content='+ ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content='�� ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content='a4 − r2 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content='+ ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content='� ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content='− 4a2 + 2Qr+ + r2 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content='+ ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content='�� ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content='× ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content='� ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content='a2 − r+ ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content='� ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content='Q + r+ ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content='��2� ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content='− δ log ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content='� ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content='� ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content='a2 − r+ ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content='� ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content='Q + r+ ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content='��2 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content='r2 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content='+ ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content='� ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content='a2 + r2 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content='+ ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content='� ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content='� ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content='+ a2 + δ log(16π) + r2 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content='+ ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content='���� ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content='a2 − r+ ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content='� ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content='Q + r+ ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content='��2�−1 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content=') ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content='× ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content='� ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content='4πr3 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content='+ ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content='� ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content='a2 + r2 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content='+ ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content='�3�−1 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content='.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content=' ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content='(26) ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content='13 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content='The Gibbs free energy is expressed as ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content='G = ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content='� ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content='− r2 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content='+ ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content='� ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content='a2 + r2 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content='+ ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content='� ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content='2� ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content='r+ ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content='� ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content='Q + r+ ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content='� ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content='− a2�� ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content='− δ log ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content='� ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content='� ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content='a2 − r+ ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content='� ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content='Q + r+ ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content='�� ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content='2 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content='r2 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content='+ ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content='� ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content='a2 + r2 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content='+ ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content='� ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content='� ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content='+ a2 + δ log(16π) + r2 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content='+ ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content='� ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content='+ r+ ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content='� ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content='a2 + r2 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content='+ ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content='� ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content='× ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content='� ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content='r+ ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content='�� ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content='a2 + r2 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content='+ ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content='�� ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content='r+ ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content='� ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content='Q + r+ ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content='� ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content='− a2�� ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content='δ ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content='� ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content='log(16π) − log ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content='� ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content='� ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content='a2 − r+ ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content='� ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content='Q + r+ ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content='�� ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content='2 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content='r2 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content='+ ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content='� ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content='a2 + r2 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content='+ ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content='� ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content='�� ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content='+ π ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content='� ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content='a2 + r2 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content='+ ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content='�� ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content='− ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content='� ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content='a4 − r2 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content='+ ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content='× ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content='� ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content='− 4a2 + 2Qr+ + r2 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content='+ ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content='��� ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content='− δ log ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content='� ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content='� ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content='a2 − r+ ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content='� ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content='Q + r+ ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content='�� ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content='2 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content='r2 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content='+ ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content='� ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content='a2 + r2 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content='+ ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content='� ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content='� ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content='+ a2 + δ log(16π) + r2 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content='+ ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content='�� ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content='+ ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content='� ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content='2r2 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content='+ ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content='� ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content='a2 + r2 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content='+ ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content='� ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content='× ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content='� ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content='− 4a2 + 3Qr+ + 2r2 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content='+ ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content='�� ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content='a2 − r+ ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content='� ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content='Q + r+ ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content='�� ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content='2� ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content='− δ log ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content='� ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content='� ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content='a2 − r+ ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content='� ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content='Q + r+ ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content='�� ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content='2 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content='r2 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content='+ ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content='� ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content='a2 + r2 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content='+ ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content='� ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content='� ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content='+ a2 + δ log(16π) + r2 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content='+ ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content='� ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content='− 2 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content='� ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content='r+ ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content='� ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content='Q + r+ ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content='� ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content='− a2�� ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content='a4 − r2 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content='+ ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content='� ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content='− 4a2 + 2Qr+ + r2 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content='+ ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content='��� ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content='− a4δ + Qr3 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content='+ ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content='� ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content='a2 + δ ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content='� ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content='− r2 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content='+ ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content='� ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content='a4 + 3a2δ ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content='� ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content='+ Qr5 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content='+ + r6 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content='+ ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content='� ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content='+ 4r2 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content='+ ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content='� ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content='a4 − r2 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content='+ ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content='� ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content='− 4a2 + 2Qr+ + r2 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content='+ ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content='��� ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content='a2 − r+ ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content='� ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content='Q + r+ ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content='��2� ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content='− δ log ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content='� ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content='� ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content='a2 − r+ ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content='� ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content='Q + r+ ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content='�� ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content='2 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content='r2 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content='+ ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content='� ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content='a2 + r2 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content='+ ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content='� ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content='� ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content='+ a2 + δ log(16π) ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content='+ r2 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content='+ ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content='� ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content='+ 2 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content='� ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content='a2 + r2 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content='+ ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content='�� ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content='a4 − r2 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content='+ ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content='� ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content='− 4a2 + 2Qr+ + r2 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content='+ ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content='��� ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content='a2 − r+ ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content='� ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content='Q + r+ ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content='��2� ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content='− δ log ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content='� ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content='� ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content='a2 − r+ ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content='� ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content='Q + r+ ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content='�� ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content='2 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content='r2 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content='+ ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content='� ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content='a2 + r2 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content='+ ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content='� ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content='� ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content='+ a2 + δ log(16π) + r2 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content='+ ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content='���� ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content='a2 − r+ ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content='� ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content='Q + r+ ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content='�� ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content='2��� ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content='4πr3 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content='+ ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content='� ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content='a2 + r2 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content='+ ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content='� ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content='3�−1 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content='.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content=' (27) [1] M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content=' Sharif, W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content=' Javed, Eur.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content=' Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content=' C 72, 1997(2012).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content=' [2] M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content=' Sharif, W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content=' Javed, Int.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content=' Mod.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content=' Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content=' Conf.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content=' Ser.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content=' 23(2013)271.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content=' [3] M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content=' Sharif, W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content=' Javed, Can.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content=' Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content=' 91(2013)236.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content=' [4] S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content=' W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content=' Hawking, Commun.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content=' Math.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content=' Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content=' 43(1975)199.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content=' [5] M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content=' K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content=' Parikh and F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content=' Wilczek, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content=' Lett.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content=' 85(2000)5042.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content=' [6] M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content=' K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content=' Parikh, Int.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content=' Mod.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content=' Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content=' D 13(2004)2351.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content=' [7] J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content=' T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content=' Firouzjaee and G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content=' F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content=' R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content=' Ellis, Gen.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content=' Rel.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content=' Grav.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content=' 47(2015)6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content=' [8] W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content=' Javed, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content=' Babar, Adv.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content=' High Energy Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content=' 2019(2019)2759641.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content=' [9] W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content=' Javed, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content=' Babar, Chinese Journal of Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content=' 61(2019)138.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content=' [10] W.' metadata={'source': 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metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content=' Babar, W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content=' Javed, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content=' ¨Ovg¨un, Mod.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content=' Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content=' Lett.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} +page_content=' A 35(2020)2050104.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdE0T4oBgHgl3EQfSACX/content/2301.02216v1.pdf'} 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