diff --git "a/E9FKT4oBgHgl3EQfaS5z/content/tmp_files/load_file.txt" "b/E9FKT4oBgHgl3EQfaS5z/content/tmp_files/load_file.txt" new file mode 100644--- /dev/null +++ "b/E9FKT4oBgHgl3EQfaS5z/content/tmp_files/load_file.txt" @@ -0,0 +1,616 @@ +filepath=/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9FKT4oBgHgl3EQfaS5z/content/2301.11807v1.pdf,len=615 +page_content='arXiv:2301.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9FKT4oBgHgl3EQfaS5z/content/2301.11807v1.pdf'} +page_content='11807v1 [physics.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9FKT4oBgHgl3EQfaS5z/content/2301.11807v1.pdf'} +page_content='gen-ph] 12 Jan 2023 Dyonic and magnetic black holes with rational nonlinear electrodynamics S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9FKT4oBgHgl3EQfaS5z/content/2301.11807v1.pdf'} +page_content=' I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9FKT4oBgHgl3EQfaS5z/content/2301.11807v1.pdf'} +page_content=' Kruglov 1 Department of Physics, University of Toronto, 60 St.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9FKT4oBgHgl3EQfaS5z/content/2301.11807v1.pdf'} +page_content=' Georges St.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9FKT4oBgHgl3EQfaS5z/content/2301.11807v1.pdf'} +page_content=', Toronto, ON M5S 1A7, Canada Canadian Quantum Research Center, 204-3002 32 Ave Vernon, BC V1T 2L7, Canada Abstract The principles of causality and unitarity are studied within rational nonlinear electrodynamics proposed earlier.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9FKT4oBgHgl3EQfaS5z/content/2301.11807v1.pdf'} +page_content=' We investigate dyonic and magnetized black holes and show that in the self-dual case, when the electric charge equals the magnetic charge, corrections to Coulomb’s law and Reissner−Nordstr¨om solutions are absent.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9FKT4oBgHgl3EQfaS5z/content/2301.11807v1.pdf'} +page_content=' In the case of the magnetic black hole, the Hawking temperature, the heat capacity and the Helmholtz free energy are calculated.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9FKT4oBgHgl3EQfaS5z/content/2301.11807v1.pdf'} +page_content=' It is shown that there are second-order phase transitions and it was demonstrated that at some range of parameters the black holes are stable.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9FKT4oBgHgl3EQfaS5z/content/2301.11807v1.pdf'} +page_content=' 1 Introduction The black holes (BHs) are real objects in the centers of many galactic and its physics is of great interest.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9FKT4oBgHgl3EQfaS5z/content/2301.11807v1.pdf'} +page_content=' Dyonic solutions in the string [1]-[4] and in the supergravity [5]-[8] theories for BHs with magnetic and electric charges were obtained.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9FKT4oBgHgl3EQfaS5z/content/2301.11807v1.pdf'} +page_content=' Such solutions are used in the theory of superconductivity and thermodynamics [9], [10], [11].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9FKT4oBgHgl3EQfaS5z/content/2301.11807v1.pdf'} +page_content=' In this paper we obtain dyonic and mag- netic BH solutions in the framework of rational nonlinear electrodynamics proposed in [12].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9FKT4oBgHgl3EQfaS5z/content/2301.11807v1.pdf'} +page_content=' The attractive feature of this nonlinear electrodynamics (NED) is the absence of singularities in the center of charges and their finite self-energy.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9FKT4oBgHgl3EQfaS5z/content/2301.11807v1.pdf'} +page_content=' Similar properties of NED were firstly observed by Born and Infeld in another NED [13].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9FKT4oBgHgl3EQfaS5z/content/2301.11807v1.pdf'} +page_content=' Quantum electrodynamics with loop corrections also leads to NED [14].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9FKT4oBgHgl3EQfaS5z/content/2301.11807v1.pdf'} +page_content=' The singularity problems are absent also in other NED models [15]-[19].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9FKT4oBgHgl3EQfaS5z/content/2301.11807v1.pdf'} +page_content=' The general relativity (GR) and the thermodynamics 1E-mail: serguei.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9FKT4oBgHgl3EQfaS5z/content/2301.11807v1.pdf'} +page_content='krouglov@utoronto.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9FKT4oBgHgl3EQfaS5z/content/2301.11807v1.pdf'} +page_content='ca 1 of BH with NED was considered in [20]-[35].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9FKT4oBgHgl3EQfaS5z/content/2301.11807v1.pdf'} +page_content=' The phase transitions in electri- cally and magnetically charged BHs were investigated in [36]-[40].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9FKT4oBgHgl3EQfaS5z/content/2301.11807v1.pdf'} +page_content=' It worth noting that the universe acceleration also can be explained by NED coupled with GR [41]-[49].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9FKT4oBgHgl3EQfaS5z/content/2301.11807v1.pdf'} +page_content=' The paper is organised as follows.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9FKT4oBgHgl3EQfaS5z/content/2301.11807v1.pdf'} +page_content=' In Sec.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9FKT4oBgHgl3EQfaS5z/content/2301.11807v1.pdf'} +page_content=' 2 we study the causality and unitarity principles.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9FKT4oBgHgl3EQfaS5z/content/2301.11807v1.pdf'} +page_content=' We obtain the dyonic solution in Sec.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9FKT4oBgHgl3EQfaS5z/content/2301.11807v1.pdf'} +page_content=' 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9FKT4oBgHgl3EQfaS5z/content/2301.11807v1.pdf'} +page_content=' In Sec.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9FKT4oBgHgl3EQfaS5z/content/2301.11807v1.pdf'} +page_content=' 4 we consider the magnetic BH.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9FKT4oBgHgl3EQfaS5z/content/2301.11807v1.pdf'} +page_content=' The metric function and their asymptotic as r → ∞ are found.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9FKT4oBgHgl3EQfaS5z/content/2301.11807v1.pdf'} +page_content=' It was shown that the magnetic mass of BHs is finite and there are not singularities of the Ricci scalar as r → ∞.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9FKT4oBgHgl3EQfaS5z/content/2301.11807v1.pdf'} +page_content=' The BH thermodynamics and the thermal stability of charged black holes are investigated in Sec.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9FKT4oBgHgl3EQfaS5z/content/2301.11807v1.pdf'} +page_content=' 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9FKT4oBgHgl3EQfaS5z/content/2301.11807v1.pdf'} +page_content=' We obtain the Hawking temperature, the heat capacity, the Helmholtz free energy and demonstrate that the phase transitions in BHs occur.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9FKT4oBgHgl3EQfaS5z/content/2301.11807v1.pdf'} +page_content=' We use units with c = 1 and the metric signature diag(−1, 1, 1, 1).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9FKT4oBgHgl3EQfaS5z/content/2301.11807v1.pdf'} +page_content=' 2 The model and principles of causality and unitarity Here, we consider rational NED, proposed in [12], with the Lagrangian den- sity L = − F 2βF + 1, (1) where the parameter β ≥ 0 possesses the dimension of (length)4, F = (1/4)FµνF µν = (B2 − E2)/2, Fµν = ∂µAν − ∂νAµ is the field tensor.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9FKT4oBgHgl3EQfaS5z/content/2301.11807v1.pdf'} +page_content=' The symmetrical energy-momentum tensor is given by [34] Tµν = − F α µ Fνα (1 + 2βF)2 − gµνL.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9FKT4oBgHgl3EQfaS5z/content/2301.11807v1.pdf'} +page_content=' (2) From Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9FKT4oBgHgl3EQfaS5z/content/2301.11807v1.pdf'} +page_content=' (2) we obtain the energy density ρ = T 0 0 = F 1 + 2βF + E2 (1 + 2βF)2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9FKT4oBgHgl3EQfaS5z/content/2301.11807v1.pdf'} +page_content=' (3) For healthy theory the general principles of causality and unitarity should hold.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9FKT4oBgHgl3EQfaS5z/content/2301.11807v1.pdf'} +page_content=' According to the causality principle the group velocity of excitations over the background has to be less than the light speed, and then tachyons are absent in the theory.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9FKT4oBgHgl3EQfaS5z/content/2301.11807v1.pdf'} +page_content=' The absence of ghosts is guaranteed by the unitarity 2 principle.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9FKT4oBgHgl3EQfaS5z/content/2301.11807v1.pdf'} +page_content=' Both principles are satisfied for the case E · B = 0 if the following inequalities hold [50]: LF ≤ 0, LFF ≥ 0, LF + 2FLFF ≤ 0, (4) where LF ≡ ∂L/∂F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9FKT4oBgHgl3EQfaS5z/content/2301.11807v1.pdf'} +page_content=' Making use of Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9FKT4oBgHgl3EQfaS5z/content/2301.11807v1.pdf'} +page_content=' (1) we obtain LF = − 1 (1 + 2βF)2, LF + 2FLFF = 6βF − 1 (1 + 2βF)3, LFF = 4β (1 + 2βF)3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9FKT4oBgHgl3EQfaS5z/content/2301.11807v1.pdf'} +page_content=' (5) With the help of Eqs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9FKT4oBgHgl3EQfaS5z/content/2301.11807v1.pdf'} +page_content=' (4) and (5), the principles of causality and unitarity take place if 6βF ≤ 1 (β ≥ 0).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9FKT4oBgHgl3EQfaS5z/content/2301.11807v1.pdf'} +page_content=' When E = 0, βB2 ≤ 1/3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9FKT4oBgHgl3EQfaS5z/content/2301.11807v1.pdf'} +page_content=' 3 The dyonic solution The action of NED coupled with GR is given by I = � d4x√−g � 1 16πGR + L � , (6) where G is Newton’s constant, 16πG ≡ M−2 P l , and MP l is the reduced Planck mass.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9FKT4oBgHgl3EQfaS5z/content/2301.11807v1.pdf'} +page_content=' The Einstein equation is Rµν − 1 2gµνR = −8πGTµν.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9FKT4oBgHgl3EQfaS5z/content/2301.11807v1.pdf'} +page_content=' (7) Varying action (6) on electromagnetic potentials we obtain the fields equation for electromagnet fields ∂µ �√−gF µνLF � = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9FKT4oBgHgl3EQfaS5z/content/2301.11807v1.pdf'} +page_content=' (8) We consider the static and spherically symmetric metric with the line element ds2 = −A(r)dt2 + 1 A(r)dr2 + r2(dϑ2 + sin2 ϑdφ2), (9) where the metric function is given by A(r) = 1 − 2M(r)G r , (10) 3 and the mass function is M(r) = m0 + � r 0 ρ(r)r2dr = m0 + mel − � ∞ r ρ(r)r2dr.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9FKT4oBgHgl3EQfaS5z/content/2301.11807v1.pdf'} +page_content=' (11) The total mass of the BH m = m0 +mel, where m0 is the Schwarzschild mass and mel = � ∞ 0 ρ(r)r2dr is the electromagnetic mass.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9FKT4oBgHgl3EQfaS5z/content/2301.11807v1.pdf'} +page_content=' The general solutions of field equations, found in [37], [38], are given by B2 = q2 m r4 , E2 = q2 e L2 Fr4, (12) where qm and qe are the magnetic and electric charges, respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9FKT4oBgHgl3EQfaS5z/content/2301.11807v1.pdf'} +page_content=' With the help of Eqs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9FKT4oBgHgl3EQfaS5z/content/2301.11807v1.pdf'} +page_content=' (1) and (12) one finds E2 = q2 e(1 + 2βF)4 r4 , (13) βF = a − b(1 + 2βF)4, a = βq2 m 2r4 , b = βq2 e 2r4 , (14) and we introduced the unitless variables a and b.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9FKT4oBgHgl3EQfaS5z/content/2301.11807v1.pdf'} +page_content=' Defining the unitless value x ≡ βF, we obtain from Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9FKT4oBgHgl3EQfaS5z/content/2301.11807v1.pdf'} +page_content=' (14) the equation as follows: b(2x + 1)4 + x − a = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9FKT4oBgHgl3EQfaS5z/content/2301.11807v1.pdf'} +page_content=' (15) Using unitless variables t = r/ 4� βq2m and n = q2 m/q2 e, one finds from Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9FKT4oBgHgl3EQfaS5z/content/2301.11807v1.pdf'} +page_content=' (15) the equation for y = 2x + 1: y4 + t4y − n − t4 = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9FKT4oBgHgl3EQfaS5z/content/2301.11807v1.pdf'} +page_content=' (16) The real dyonic solution to Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9FKT4oBgHgl3EQfaS5z/content/2301.11807v1.pdf'} +page_content=' (16) is y = � � � � � 4√ 3t4 4 4√ n + t4 � sinh(ϕ/3) − √ n + t4 sinh(ϕ/3) √ 3 − � sinh(ϕ/3) 4√ n + t4 4√ 3 , sinh(ϕ) = 33/2t8 16(n + t4)3/2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9FKT4oBgHgl3EQfaS5z/content/2301.11807v1.pdf'} +page_content=' (17) Putting n = 0 in Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9FKT4oBgHgl3EQfaS5z/content/2301.11807v1.pdf'} +page_content=' (17) we come to the solution corresponding to the electrically charged BH [34].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9FKT4oBgHgl3EQfaS5z/content/2301.11807v1.pdf'} +page_content=' We find the self-dual solution at qe = qm (a = b) 4 from Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9FKT4oBgHgl3EQfaS5z/content/2301.11807v1.pdf'} +page_content=' (15).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9FKT4oBgHgl3EQfaS5z/content/2301.11807v1.pdf'} +page_content=' Then x = 0 (F = 0, E = B), E = q/r2 (q ≡ qe = qm) and with the help of Eqs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9FKT4oBgHgl3EQfaS5z/content/2301.11807v1.pdf'} +page_content=' (3) and (11) we obtain the mass function M(r) = m − � ∞ r ρ(r)r2dr = m − q2 r .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9FKT4oBgHgl3EQfaS5z/content/2301.11807v1.pdf'} +page_content=' (18) Making use of Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9FKT4oBgHgl3EQfaS5z/content/2301.11807v1.pdf'} +page_content=' (10) one finds the metric function A(r) = 1 − 2mG r + 2q2G r2 .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9FKT4oBgHgl3EQfaS5z/content/2301.11807v1.pdf'} +page_content=' (19) The metric function (19) corresponds to the Reissner−Nordst¨om (RN) solu- tion with 2q2 = q2 e + q2 m.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9FKT4oBgHgl3EQfaS5z/content/2301.11807v1.pdf'} +page_content=' 4 The magnetic black hole Let us consider the static magnetic BH 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9FKT4oBgHgl3EQfaS5z/content/2301.11807v1.pdf'} +page_content=' Taking into account that qe = 0, F = q2 m/(2r4), we obtain from Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9FKT4oBgHgl3EQfaS5z/content/2301.11807v1.pdf'} +page_content=' (3) the magnetic energy density ρM = B2 2(βB2 + 1) = q2 m 2(r4 + βq2 m).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9FKT4oBgHgl3EQfaS5z/content/2301.11807v1.pdf'} +page_content=' (20) With the help of Eqs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9FKT4oBgHgl3EQfaS5z/content/2301.11807v1.pdf'} +page_content=' (11) and (20) one finds the mass function M(x) = m0 + q3/2 m 8 √ 2β1/4 � ln x2 − √ 2x + 1 x2 + √ 2x + 1 +2 arctan( √ 2x + 1) − 2 arctan(1 − √ 2x) � , (21) where x = r/ 4� βq2m.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9FKT4oBgHgl3EQfaS5z/content/2301.11807v1.pdf'} +page_content=' The BH magnetic mass is given by mM = � ∞ 0 ρM(r)r2dr = πq3/2 m 4 √ 2β1/4 ≈ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9FKT4oBgHgl3EQfaS5z/content/2301.11807v1.pdf'} +page_content='56 q3/2 m β1/4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9FKT4oBgHgl3EQfaS5z/content/2301.11807v1.pdf'} +page_content=' (22) 2In the paper M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9FKT4oBgHgl3EQfaS5z/content/2301.11807v1.pdf'} +page_content='-S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9FKT4oBgHgl3EQfaS5z/content/2301.11807v1.pdf'} +page_content=' Ma, Ann.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9FKT4oBgHgl3EQfaS5z/content/2301.11807v1.pdf'} +page_content=' Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9FKT4oBgHgl3EQfaS5z/content/2301.11807v1.pdf'} +page_content=' 362, 529 (2015) the author also considered the static magnetic BH based on NED proposed in [12].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9FKT4oBgHgl3EQfaS5z/content/2301.11807v1.pdf'} +page_content=' However, here we use unitless variables that are more convenient for the analyses of the BH thermodynamics.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9FKT4oBgHgl3EQfaS5z/content/2301.11807v1.pdf'} +page_content=' In addition, we analyse more general case when the BH besides the electromagnetic mass possesses the Schwarzschild mass (having non-electromagnetic nature).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9FKT4oBgHgl3EQfaS5z/content/2301.11807v1.pdf'} +page_content=' 5 The Schwarzschild mass m0 is a free parameter and at qm = 0 one has mM = 0, and we arrive at the Schwarzschild BH.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9FKT4oBgHgl3EQfaS5z/content/2301.11807v1.pdf'} +page_content=' Making use of Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9FKT4oBgHgl3EQfaS5z/content/2301.11807v1.pdf'} +page_content=' (10) we obtain the metric function A(x) = 1 − 2m0G 4� βq2 mx − qmG 4√2βx � ln x2 − √ 2x + 1 x2 + √ 2x + 1 +2 arctan( √ 2x + 1) − 2 arctan(1 − √ 2x) � , (23) As r → ∞ the metric function (23) becomes A(r) = 1 − 2mG r + q2 mG r2 + O(r−5) r → ∞, (24) where m = m0 + mM.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9FKT4oBgHgl3EQfaS5z/content/2301.11807v1.pdf'} +page_content=' The correction to the RN solution, according to Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9FKT4oBgHgl3EQfaS5z/content/2301.11807v1.pdf'} +page_content=' (24), is in the order of O(r−5).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9FKT4oBgHgl3EQfaS5z/content/2301.11807v1.pdf'} +page_content=' At m0 = 0 and r → 0, from Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9FKT4oBgHgl3EQfaS5z/content/2301.11807v1.pdf'} +page_content=' (23) one finds the asymptotic with a de Sitter core A(r) = 1 − Gr2 β + Gr6 7β2q2 m − Gr10 11β3q4 m + O(r12) r → 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9FKT4oBgHgl3EQfaS5z/content/2301.11807v1.pdf'} +page_content=' (25) The solution (25) is regular because as r → 0 we have A(r) → 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9FKT4oBgHgl3EQfaS5z/content/2301.11807v1.pdf'} +page_content=' When m0 ̸= 0 the solution is singular and A(r) → ∞.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9FKT4oBgHgl3EQfaS5z/content/2301.11807v1.pdf'} +page_content=' Let us introduce unitless constants C = m0G/(β1/4√qm), B = qmG/√β.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9FKT4oBgHgl3EQfaS5z/content/2301.11807v1.pdf'} +page_content=' Then the horizon radii, that are the roots of the equation A(r) = 0 (x+/− = r+/−/(√qmβ1/4)), are given in Tables 1 and 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9FKT4oBgHgl3EQfaS5z/content/2301.11807v1.pdf'} +page_content=' The plots of the metric function (23) are depicted in Table 1: B = 1 C 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9FKT4oBgHgl3EQfaS5z/content/2301.11807v1.pdf'} +page_content='6 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9FKT4oBgHgl3EQfaS5z/content/2301.11807v1.pdf'} +page_content='7 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9FKT4oBgHgl3EQfaS5z/content/2301.11807v1.pdf'} +page_content='8 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9FKT4oBgHgl3EQfaS5z/content/2301.11807v1.pdf'} +page_content='9 1 2 3 4 5 x+ 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9FKT4oBgHgl3EQfaS5z/content/2301.11807v1.pdf'} +page_content='75 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9FKT4oBgHgl3EQfaS5z/content/2301.11807v1.pdf'} +page_content='02 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9FKT4oBgHgl3EQfaS5z/content/2301.11807v1.pdf'} +page_content='27 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9FKT4oBgHgl3EQfaS5z/content/2301.11807v1.pdf'} +page_content='52 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9FKT4oBgHgl3EQfaS5z/content/2301.11807v1.pdf'} +page_content='75 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9FKT4oBgHgl3EQfaS5z/content/2301.11807v1.pdf'} +page_content='91 6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9FKT4oBgHgl3EQfaS5z/content/2301.11807v1.pdf'} +page_content='97 9.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9FKT4oBgHgl3EQfaS5z/content/2301.11807v1.pdf'} +page_content='00 11.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9FKT4oBgHgl3EQfaS5z/content/2301.11807v1.pdf'} +page_content='02 Figs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9FKT4oBgHgl3EQfaS5z/content/2301.11807v1.pdf'} +page_content=' 1 and 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9FKT4oBgHgl3EQfaS5z/content/2301.11807v1.pdf'} +page_content=' According to Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9FKT4oBgHgl3EQfaS5z/content/2301.11807v1.pdf'} +page_content=' 1 at m0 ̸= 0 (B = 1) there is only one horizon.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9FKT4oBgHgl3EQfaS5z/content/2301.11807v1.pdf'} +page_content=' For the bigger mass (the parameter C is greater) the horizon radius increases.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9FKT4oBgHgl3EQfaS5z/content/2301.11807v1.pdf'} +page_content=' Figure 2 shows that there are no horizons at m0 = 0, B < 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9FKT4oBgHgl3EQfaS5z/content/2301.11807v1.pdf'} +page_content='17), an extreme horizon occurs at m0 = 0, B ≈ 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9FKT4oBgHgl3EQfaS5z/content/2301.11807v1.pdf'} +page_content='173, and two horizons hold at m0 = 0 and B > 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9FKT4oBgHgl3EQfaS5z/content/2301.11807v1.pdf'} +page_content='173.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9FKT4oBgHgl3EQfaS5z/content/2301.11807v1.pdf'} +page_content=' Making use of Eqs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9FKT4oBgHgl3EQfaS5z/content/2301.11807v1.pdf'} +page_content=' (2) and (7) at E = 0, we obtain the Ricci scalar R = 8πGT µ µ = 16πGβq4 m (r4 + βq2 m)2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9FKT4oBgHgl3EQfaS5z/content/2301.11807v1.pdf'} +page_content=' (26) The Ricci scalar approaches to zero as r → ∞ and spacetime becomes flat.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9FKT4oBgHgl3EQfaS5z/content/2301.11807v1.pdf'} +page_content=' 6 Table 2: m0 = 0 B 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9FKT4oBgHgl3EQfaS5z/content/2301.11807v1.pdf'} +page_content='173 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9FKT4oBgHgl3EQfaS5z/content/2301.11807v1.pdf'} +page_content='2 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9FKT4oBgHgl3EQfaS5z/content/2301.11807v1.pdf'} +page_content='5 4 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9FKT4oBgHgl3EQfaS5z/content/2301.11807v1.pdf'} +page_content='5 5 6 7 8 x− 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9FKT4oBgHgl3EQfaS5z/content/2301.11807v1.pdf'} +page_content='68 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9FKT4oBgHgl3EQfaS5z/content/2301.11807v1.pdf'} +page_content='52 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9FKT4oBgHgl3EQfaS5z/content/2301.11807v1.pdf'} +page_content='21 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9FKT4oBgHgl3EQfaS5z/content/2301.11807v1.pdf'} +page_content='03 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9FKT4oBgHgl3EQfaS5z/content/2301.11807v1.pdf'} +page_content='92 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9FKT4oBgHgl3EQfaS5z/content/2301.11807v1.pdf'} +page_content='85 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9FKT4oBgHgl3EQfaS5z/content/2301.11807v1.pdf'} +page_content='75 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9FKT4oBgHgl3EQfaS5z/content/2301.11807v1.pdf'} +page_content='68 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9FKT4oBgHgl3EQfaS5z/content/2301.11807v1.pdf'} +page_content='63 x+ 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9FKT4oBgHgl3EQfaS5z/content/2301.11807v1.pdf'} +page_content='68 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9FKT4oBgHgl3EQfaS5z/content/2301.11807v1.pdf'} +page_content='87 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9FKT4oBgHgl3EQfaS5z/content/2301.11807v1.pdf'} +page_content='49 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9FKT4oBgHgl3EQfaS5z/content/2301.11807v1.pdf'} +page_content='19 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9FKT4oBgHgl3EQfaS5z/content/2301.11807v1.pdf'} +page_content='82 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9FKT4oBgHgl3EQfaS5z/content/2301.11807v1.pdf'} +page_content='42 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9FKT4oBgHgl3EQfaS5z/content/2301.11807v1.pdf'} +page_content='59 6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9FKT4oBgHgl3EQfaS5z/content/2301.11807v1.pdf'} +page_content='74 7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9FKT4oBgHgl3EQfaS5z/content/2301.11807v1.pdf'} +page_content='87 0 2 4 6 8 10 −20 −15 −10 −5 0 5 x A(x) C= 1 C= 2 C= 3 Figure 1: The plot of the function A(x) for B = 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9FKT4oBgHgl3EQfaS5z/content/2301.11807v1.pdf'} +page_content=' The solid curve is for C = 1, the dashed curve corresponds to C = 2, and the dashed-doted curve corresponds to C = 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9FKT4oBgHgl3EQfaS5z/content/2301.11807v1.pdf'} +page_content=' 5 The black hole thermodynamics To study the black holes thermodynamics and the thermal stability of mag- netic BHs, we consider the Hawking temperature TH = κ 2π = A′(r+) 4π , (27) where κ is the surface gravity and r+ is the event horizon radius.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9FKT4oBgHgl3EQfaS5z/content/2301.11807v1.pdf'} +page_content=' With the help of Eqs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9FKT4oBgHgl3EQfaS5z/content/2301.11807v1.pdf'} +page_content=' (10) and (11) one finds the relations A′(r) = 2GM(r) r2 − 2GM′(r) r , M′(r) = r2ρ, M(r+) = r+ 2G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9FKT4oBgHgl3EQfaS5z/content/2301.11807v1.pdf'} +page_content=' (28) Making use of Eqs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9FKT4oBgHgl3EQfaS5z/content/2301.11807v1.pdf'} +page_content=' (3), (27) and (28) we obtain the Hawking temperature TH = 1 4π � 1 r+ − 2Gr+ρ(r+) � = 1 4πβ1/4√qm � 1 x+ − Gqmx+ √β(1 + x4+) � .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9FKT4oBgHgl3EQfaS5z/content/2301.11807v1.pdf'} +page_content=' (29) 7 0 1 2 3 4 5 6 7 8 −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9FKT4oBgHgl3EQfaS5z/content/2301.11807v1.pdf'} +page_content='6 −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9FKT4oBgHgl3EQfaS5z/content/2301.11807v1.pdf'} +page_content='4 −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9FKT4oBgHgl3EQfaS5z/content/2301.11807v1.pdf'} +page_content='2 0 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9FKT4oBgHgl3EQfaS5z/content/2301.11807v1.pdf'} +page_content='2 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9FKT4oBgHgl3EQfaS5z/content/2301.11807v1.pdf'} +page_content='4 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9FKT4oBgHgl3EQfaS5z/content/2301.11807v1.pdf'} +page_content='6 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9FKT4oBgHgl3EQfaS5z/content/2301.11807v1.pdf'} +page_content='8 1 x A(x) B= 2 B= 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9FKT4oBgHgl3EQfaS5z/content/2301.11807v1.pdf'} +page_content='175 B= 5 Figure 2: The plot of the function A(x) for m0 = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9FKT4oBgHgl3EQfaS5z/content/2301.11807v1.pdf'} +page_content=' The solid curve is for B = 2, the dashed curve corresponds to B = 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9FKT4oBgHgl3EQfaS5z/content/2301.11807v1.pdf'} +page_content='175, and the dashed-doted curve corresponds to B = 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9FKT4oBgHgl3EQfaS5z/content/2301.11807v1.pdf'} +page_content=' Using the equation M(r+) = r+/(2G) and (21) we find Gqm √β = 4 √ 2(x+ − 2C) D , D ≡ ln x2 − √ 2x + 1 x2 + √ 2x + 1 − 2 arctan(1 − √ 2x) + 2 arctan(1 + √ 2x).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9FKT4oBgHgl3EQfaS5z/content/2301.11807v1.pdf'} +page_content=' (30) Replacing Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9FKT4oBgHgl3EQfaS5z/content/2301.11807v1.pdf'} +page_content=' (30) into Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9FKT4oBgHgl3EQfaS5z/content/2301.11807v1.pdf'} +page_content=' (29) one obtains the Hawking temperature as follows: TH == 1 4πβ1/4√qm � 1 x+ − 4 √ 2(x+ − 2C)x+ (1 + x4 +)D � .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9FKT4oBgHgl3EQfaS5z/content/2301.11807v1.pdf'} +page_content=' (31) The plots of the functions TH(x+)√qmβ1/4 are depicted in Figs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9FKT4oBgHgl3EQfaS5z/content/2301.11807v1.pdf'} +page_content=' 3 and 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9FKT4oBgHgl3EQfaS5z/content/2301.11807v1.pdf'} +page_content=' According to Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9FKT4oBgHgl3EQfaS5z/content/2301.11807v1.pdf'} +page_content=' 3 the temperature is positive everywhere for the case C ̸= 0 (m0 ̸= 0).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9FKT4oBgHgl3EQfaS5z/content/2301.11807v1.pdf'} +page_content=' Figure 4 shows that the Hawking temperature for C = 0 (m0 = 0) is positive for x+ > 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9FKT4oBgHgl3EQfaS5z/content/2301.11807v1.pdf'} +page_content='679 and is zero at x+ ≈ 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9FKT4oBgHgl3EQfaS5z/content/2301.11807v1.pdf'} +page_content='679 .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9FKT4oBgHgl3EQfaS5z/content/2301.11807v1.pdf'} +page_content=' The BH is unstable when the temperature is negative.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9FKT4oBgHgl3EQfaS5z/content/2301.11807v1.pdf'} +page_content=' From Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9FKT4oBgHgl3EQfaS5z/content/2301.11807v1.pdf'} +page_content=' (30) we obtain the value of Gqm/√β = 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9FKT4oBgHgl3EQfaS5z/content/2301.11807v1.pdf'} +page_content='173 corresponding to x+ = 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9FKT4oBgHgl3EQfaS5z/content/2301.11807v1.pdf'} +page_content='679.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9FKT4oBgHgl3EQfaS5z/content/2301.11807v1.pdf'} +page_content=' By studying the signs of the heat capacity and the Helmholtz free energy, we can observe the different stability phases of the BH [51].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9FKT4oBgHgl3EQfaS5z/content/2301.11807v1.pdf'} +page_content=' Making use of the Hawking entropy of the BH S = Area/(4G) = πr2 +/G = πx2 +qm √β/G we find the heat capacity Cq = TH � ���S ∂TH � q = TH∂S/∂x+ ∂TH/∂x+ = 2πqm √βx+TH G∂TH/∂x+ .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9FKT4oBgHgl3EQfaS5z/content/2301.11807v1.pdf'} +page_content=' (32) 8 0 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9FKT4oBgHgl3EQfaS5z/content/2301.11807v1.pdf'} +page_content='5 1 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9FKT4oBgHgl3EQfaS5z/content/2301.11807v1.pdf'} +page_content='5 2 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9FKT4oBgHgl3EQfaS5z/content/2301.11807v1.pdf'} +page_content='5 3 0 50 100 150 x+ (qm 2 β)1/4TH C= 1 C= 2 C= 3 Figure 3: The plot of the function TH√qmβ1/4 vs x+.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9FKT4oBgHgl3EQfaS5z/content/2301.11807v1.pdf'} +page_content=' The solid curve is for C = 1, the dashed curve corresponds to C = 2, and the dashed-doted curve corresponds to C = 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9FKT4oBgHgl3EQfaS5z/content/2301.11807v1.pdf'} +page_content=' According to Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9FKT4oBgHgl3EQfaS5z/content/2301.11807v1.pdf'} +page_content=' (32) the heat capacity possesses a singularity when the Hawking temperature has an extremum (∂TH/∂x+ = 0).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9FKT4oBgHgl3EQfaS5z/content/2301.11807v1.pdf'} +page_content=' The plots of the heat capacity versus the variable x+ for different parameters C are depicted in Figs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9FKT4oBgHgl3EQfaS5z/content/2301.11807v1.pdf'} +page_content=' 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9FKT4oBgHgl3EQfaS5z/content/2301.11807v1.pdf'} +page_content=' 6, and 7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9FKT4oBgHgl3EQfaS5z/content/2301.11807v1.pdf'} +page_content=' Figure 5 shows the Schwarzschild behaviour of the heat capacity for C ̸= 0 (m0 ̸= 0), i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9FKT4oBgHgl3EQfaS5z/content/2301.11807v1.pdf'} +page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9FKT4oBgHgl3EQfaS5z/content/2301.11807v1.pdf'} +page_content=' it is negative at ∂TH/∂x+ < 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9FKT4oBgHgl3EQfaS5z/content/2301.11807v1.pdf'} +page_content=' As a result, the BHs are unstable for the case m0 ̸= 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9FKT4oBgHgl3EQfaS5z/content/2301.11807v1.pdf'} +page_content=' In accordance with Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9FKT4oBgHgl3EQfaS5z/content/2301.11807v1.pdf'} +page_content=' 6 the BH is unstable at 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9FKT4oBgHgl3EQfaS5z/content/2301.11807v1.pdf'} +page_content='679 > x > 0 because the heat capacity is negative.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9FKT4oBgHgl3EQfaS5z/content/2301.11807v1.pdf'} +page_content=' Figure 7 shows a singularity in the heat capacity at the point x ≈ 3 where the second-order phase transition occurs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9FKT4oBgHgl3EQfaS5z/content/2301.11807v1.pdf'} +page_content=' When m0 = 0 the heat capacity is positive at the range 3 > x > 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9FKT4oBgHgl3EQfaS5z/content/2301.11807v1.pdf'} +page_content='679 and the BH is stable.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9FKT4oBgHgl3EQfaS5z/content/2301.11807v1.pdf'} +page_content=' To complete the analysis of phase transitions we consider the Helmholtz free energy which is given by F = m − THS.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9FKT4oBgHgl3EQfaS5z/content/2301.11807v1.pdf'} +page_content=' (33) The mass of the BH m plays the role of the internal energy, and the Hawking entropy is S = πr2 +/G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9FKT4oBgHgl3EQfaS5z/content/2301.11807v1.pdf'} +page_content=' Making use of Eqs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9FKT4oBgHgl3EQfaS5z/content/2301.11807v1.pdf'} +page_content=' (22).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9FKT4oBgHgl3EQfaS5z/content/2301.11807v1.pdf'} +page_content=' (31) and (33) we obtain GF √qmβ1/4 = B � C + π 4 √ 2 � − x+ 4 + √ 2x2 +(x+ − 2C) (x4 + + 1)D .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9FKT4oBgHgl3EQfaS5z/content/2301.11807v1.pdf'} +page_content=' (34) Substituting B = qmG/√β from Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9FKT4oBgHgl3EQfaS5z/content/2301.11807v1.pdf'} +page_content=' (30) into (34) we find GF √qmβ1/4 = � C + π 4 √ 2 � 4 √ 2(x+ − 2C) D − x+ 4 + √ 2x2 +(x+ − 2C) (x4+ + 1)D � .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9FKT4oBgHgl3EQfaS5z/content/2301.11807v1.pdf'} +page_content=' (35) 9 1 2 3 4 5 6 7 8 9 10 −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9FKT4oBgHgl3EQfaS5z/content/2301.11807v1.pdf'} +page_content='1 −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9FKT4oBgHgl3EQfaS5z/content/2301.11807v1.pdf'} +page_content='08 −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9FKT4oBgHgl3EQfaS5z/content/2301.11807v1.pdf'} +page_content='06 −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9FKT4oBgHgl3EQfaS5z/content/2301.11807v1.pdf'} +page_content='04 −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9FKT4oBgHgl3EQfaS5z/content/2301.11807v1.pdf'} +page_content='02 0 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9FKT4oBgHgl3EQfaS5z/content/2301.11807v1.pdf'} +page_content='02 x+ (qm 2 β)1/4TH Figure 4: The plot of the function TH√qmβ1/4 vs x+ for C = 0 (m0 = 0).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9FKT4oBgHgl3EQfaS5z/content/2301.11807v1.pdf'} +page_content=' The plots of the unitless reduced free energy GF/(√qmβ1/4) vs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9FKT4oBgHgl3EQfaS5z/content/2301.11807v1.pdf'} +page_content=' x+ are depicted in Figs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9FKT4oBgHgl3EQfaS5z/content/2301.11807v1.pdf'} +page_content=' 8 and 9.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9FKT4oBgHgl3EQfaS5z/content/2301.11807v1.pdf'} +page_content=' The BHs with F > 0, Cq < 0 are unstable and the BHs with F < 0, Cq > 0 are stable.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9FKT4oBgHgl3EQfaS5z/content/2301.11807v1.pdf'} +page_content=' In accordance with Figs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9FKT4oBgHgl3EQfaS5z/content/2301.11807v1.pdf'} +page_content=' 5-9, there are other phases with F > 0, Cq > 0 and F < 0, Cq < 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9FKT4oBgHgl3EQfaS5z/content/2301.11807v1.pdf'} +page_content=' In the case F < 0, Cq < 0 the BHs are less energetic than the pure radiation and, as a result, BHs do not decay through tunneling.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9FKT4oBgHgl3EQfaS5z/content/2301.11807v1.pdf'} +page_content=' For large masses of BHs (C > 1) this phase holds.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9FKT4oBgHgl3EQfaS5z/content/2301.11807v1.pdf'} +page_content=' Because the heat capacities are negative, the BH temperature decreases when the mass of BH increases.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9FKT4oBgHgl3EQfaS5z/content/2301.11807v1.pdf'} +page_content=' Such phases are also realised in another model [52].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9FKT4oBgHgl3EQfaS5z/content/2301.11807v1.pdf'} +page_content=' 6 Conclusion The correspondence principle of the NED model holds as for weak fields our model is converted into Maxwell’s electrodynamics.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9FKT4oBgHgl3EQfaS5z/content/2301.11807v1.pdf'} +page_content=' It was demonstrated that at βB2 ≤ 1/3 (E = 0) the principles of causality and unitarity take place.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9FKT4oBgHgl3EQfaS5z/content/2301.11807v1.pdf'} +page_content=' In this model the singularity of the electric field at the center of charges is absent and the maximum electric field in the origin is E(0) = 1/√β.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9FKT4oBgHgl3EQfaS5z/content/2301.11807v1.pdf'} +page_content=' The dyonic and magnetic BHs in GR were studied.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9FKT4oBgHgl3EQfaS5z/content/2301.11807v1.pdf'} +page_content=' It was shown that in the self-dual case (qe = qm) the corrections to Coulomb’s law and RN solutions are absent.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9FKT4oBgHgl3EQfaS5z/content/2301.11807v1.pdf'} +page_content=' The Ricci scalar does not have the singularity and as r → ∞ space-time becomes flat.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9FKT4oBgHgl3EQfaS5z/content/2301.11807v1.pdf'} +page_content=' The thermodynamics and the thermal stability of magnetized BHs were investigated.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9FKT4oBgHgl3EQfaS5z/content/2301.11807v1.pdf'} +page_content=' The Hawking temperature, the heat capacity and the Helmholtz free energy of BHs were calculated.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9FKT4oBgHgl3EQfaS5z/content/2301.11807v1.pdf'} +page_content=' It was demonstrated that the heat capac- 10 0 2 4 6 8 10 −700 −600 −500 −400 −300 −200 −100 0 x+ GCq/(qmβ0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9FKT4oBgHgl3EQfaS5z/content/2301.11807v1.pdf'} +page_content='5) C= 1 C= 2 C= 3 Figure 5: The plot of the function GCq/(q2 mβ)1/2 vs x+.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9FKT4oBgHgl3EQfaS5z/content/2301.11807v1.pdf'} +page_content=' The solid curve is for C = 1, the dashed curve corresponds to C = 2, and the dashed-doted curve corresponds to C = 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9FKT4oBgHgl3EQfaS5z/content/2301.11807v1.pdf'} +page_content=' 0 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9FKT4oBgHgl3EQfaS5z/content/2301.11807v1.pdf'} +page_content='5 1 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9FKT4oBgHgl3EQfaS5z/content/2301.11807v1.pdf'} +page_content='5 2 −3 −2 −1 0 1 2 3 4 5 6 7 x+ GCq/(qmβ1/2) Figure 6: The plot of the function GCq/(q2 mβ)1/2 vs x+ for C = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9FKT4oBgHgl3EQfaS5z/content/2301.11807v1.pdf'} +page_content=' ity diverges at some event radii r+ (x+) for the case when the total BH mass is the magnetic mass and the phase transitions of the second-order occurs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9FKT4oBgHgl3EQfaS5z/content/2301.11807v1.pdf'} +page_content=' We shown that there is a new stability region of BH solutions when the heat capacity and the free energy are negative.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9FKT4oBgHgl3EQfaS5z/content/2301.11807v1.pdf'} +page_content=' In this case BHs are less energetic than the pure radiation and BHs do not decay via tunneling.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9FKT4oBgHgl3EQfaS5z/content/2301.11807v1.pdf'} +page_content=' References [1] A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9FKT4oBgHgl3EQfaS5z/content/2301.11807v1.pdf'} +page_content=' D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9FKT4oBgHgl3EQfaS5z/content/2301.11807v1.pdf'} +page_content=' Shapere, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9FKT4oBgHgl3EQfaS5z/content/2301.11807v1.pdf'} +page_content=' Trivedi, and F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9FKT4oBgHgl3EQfaS5z/content/2301.11807v1.pdf'} +page_content=' Wilczek, Mod.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9FKT4oBgHgl3EQfaS5z/content/2301.11807v1.pdf'} +page_content=' Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9FKT4oBgHgl3EQfaS5z/content/2301.11807v1.pdf'} +page_content=' Lett.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9FKT4oBgHgl3EQfaS5z/content/2301.11807v1.pdf'} +page_content=' A 6, 2677 (1991).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9FKT4oBgHgl3EQfaS5z/content/2301.11807v1.pdf'} +page_content=' 11 2 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9FKT4oBgHgl3EQfaS5z/content/2301.11807v1.pdf'} +page_content='5 3 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9FKT4oBgHgl3EQfaS5z/content/2301.11807v1.pdf'} +page_content='5 4 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9FKT4oBgHgl3EQfaS5z/content/2301.11807v1.pdf'} +page_content='5 5 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9FKT4oBgHgl3EQfaS5z/content/2301.11807v1.pdf'} +page_content='5 6 −2000 −1500 −1000 −500 0 500 1000 1500 2000 2500 x+ GCq/(qmβ0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9FKT4oBgHgl3EQfaS5z/content/2301.11807v1.pdf'} +page_content='5) Figure 7: The plot of the function GCq/(q2 mβ)1/2 vs x+ for C = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9FKT4oBgHgl3EQfaS5z/content/2301.11807v1.pdf'} +page_content=' 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9FKT4oBgHgl3EQfaS5z/content/2301.11807v1.pdf'} +page_content='2 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9FKT4oBgHgl3EQfaS5z/content/2301.11807v1.pdf'} +page_content='4 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9FKT4oBgHgl3EQfaS5z/content/2301.11807v1.pdf'} +page_content='6 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9FKT4oBgHgl3EQfaS5z/content/2301.11807v1.pdf'} +page_content='8 1 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9FKT4oBgHgl3EQfaS5z/content/2301.11807v1.pdf'} +page_content='2 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9FKT4oBgHgl3EQfaS5z/content/2301.11807v1.pdf'} +page_content='4 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9FKT4oBgHgl3EQfaS5z/content/2301.11807v1.pdf'} +page_content='6 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9FKT4oBgHgl3EQfaS5z/content/2301.11807v1.pdf'} +page_content='8 2 −14000 −12000 −10000 −8000 −6000 −4000 −2000 0 x+ GF/(qm 2 β)1/4 C= 1 C= 2 C= 4 Figure 8: The plot of the function GF/(√qmβ1/4) vs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9FKT4oBgHgl3EQfaS5z/content/2301.11807v1.pdf'} +page_content=' x+.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9FKT4oBgHgl3EQfaS5z/content/2301.11807v1.pdf'} +page_content=' The dashed curve corresponds to C = 2, the solid curve is for C = 1, and the dashed-doted curve corresponds to C = 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9FKT4oBgHgl3EQfaS5z/content/2301.11807v1.pdf'} +page_content=' [2] S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9FKT4oBgHgl3EQfaS5z/content/2301.11807v1.pdf'} +page_content=' Mignemi, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9FKT4oBgHgl3EQfaS5z/content/2301.11807v1.pdf'} +page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9FKT4oBgHgl3EQfaS5z/content/2301.11807v1.pdf'} +page_content=' D 51, 934 (1995).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9FKT4oBgHgl3EQfaS5z/content/2301.11807v1.pdf'} +page_content=' [3] M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9FKT4oBgHgl3EQfaS5z/content/2301.11807v1.pdf'} +page_content=' Cvetic and A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9FKT4oBgHgl3EQfaS5z/content/2301.11807v1.pdf'} +page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9FKT4oBgHgl3EQfaS5z/content/2301.11807v1.pdf'} +page_content=' Tseytlin, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9FKT4oBgHgl3EQfaS5z/content/2301.11807v1.pdf'} +page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9FKT4oBgHgl3EQfaS5z/content/2301.11807v1.pdf'} +page_content=' D 53, 5619 (1996);' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9FKT4oBgHgl3EQfaS5z/content/2301.11807v1.pdf'} +page_content=' Erratum: Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9FKT4oBgHgl3EQfaS5z/content/2301.11807v1.pdf'} +page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9FKT4oBgHgl3EQfaS5z/content/2301.11807v1.pdf'} +page_content=' D 55, 3907 (1997).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9FKT4oBgHgl3EQfaS5z/content/2301.11807v1.pdf'} +page_content=' [4] D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9FKT4oBgHgl3EQfaS5z/content/2301.11807v1.pdf'} +page_content=' P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9FKT4oBgHgl3EQfaS5z/content/2301.11807v1.pdf'} +page_content=' Jatkar, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9FKT4oBgHgl3EQfaS5z/content/2301.11807v1.pdf'} +page_content=' Mukherji, and S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9FKT4oBgHgl3EQfaS5z/content/2301.11807v1.pdf'} +page_content=' Panda, Nucl.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9FKT4oBgHgl3EQfaS5z/content/2301.11807v1.pdf'} +page_content=' Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9FKT4oBgHgl3EQfaS5z/content/2301.11807v1.pdf'} +page_content=' B 484, 223 (1997).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9FKT4oBgHgl3EQfaS5z/content/2301.11807v1.pdf'} +page_content=' [5] A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9FKT4oBgHgl3EQfaS5z/content/2301.11807v1.pdf'} +page_content=' H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9FKT4oBgHgl3EQfaS5z/content/2301.11807v1.pdf'} +page_content=' Chamseddine and W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9FKT4oBgHgl3EQfaS5z/content/2301.11807v1.pdf'} +page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9FKT4oBgHgl3EQfaS5z/content/2301.11807v1.pdf'} +page_content=' Sabra, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9FKT4oBgHgl3EQfaS5z/content/2301.11807v1.pdf'} +page_content=' Lett.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9FKT4oBgHgl3EQfaS5z/content/2301.11807v1.pdf'} +page_content=' B 485, 301 (2000).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9FKT4oBgHgl3EQfaS5z/content/2301.11807v1.pdf'} +page_content=' [6] D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9FKT4oBgHgl3EQfaS5z/content/2301.11807v1.pdf'} +page_content=' D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9FKT4oBgHgl3EQfaS5z/content/2301.11807v1.pdf'} +page_content=' K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9FKT4oBgHgl3EQfaS5z/content/2301.11807v1.pdf'} +page_content=' Chow and G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9FKT4oBgHgl3EQfaS5z/content/2301.11807v1.pdf'} +page_content=' Compere, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9FKT4oBgHgl3EQfaS5z/content/2301.11807v1.pdf'} +page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9FKT4oBgHgl3EQfaS5z/content/2301.11807v1.pdf'} +page_content=' D 89, 065003 (2014).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9FKT4oBgHgl3EQfaS5z/content/2301.11807v1.pdf'} +page_content=' [7] P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9FKT4oBgHgl3EQfaS5z/content/2301.11807v1.pdf'} +page_content=' Meessen, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9FKT4oBgHgl3EQfaS5z/content/2301.11807v1.pdf'} +page_content=' Ortin, and P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9FKT4oBgHgl3EQfaS5z/content/2301.11807v1.pdf'} +page_content=' F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9FKT4oBgHgl3EQfaS5z/content/2301.11807v1.pdf'} +page_content=' Ramirez, JHEP 1710, 066 (2017).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9FKT4oBgHgl3EQfaS5z/content/2301.11807v1.pdf'} +page_content=' [8] H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9FKT4oBgHgl3EQfaS5z/content/2301.11807v1.pdf'} +page_content=' Lu, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9FKT4oBgHgl3EQfaS5z/content/2301.11807v1.pdf'} +page_content=' Pang, and C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9FKT4oBgHgl3EQfaS5z/content/2301.11807v1.pdf'} +page_content='N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9FKT4oBgHgl3EQfaS5z/content/2301.11807v1.pdf'} +page_content=' Pope, JHEP 1311, 033 (2013).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9FKT4oBgHgl3EQfaS5z/content/2301.11807v1.pdf'} +page_content=' 12 0 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9FKT4oBgHgl3EQfaS5z/content/2301.11807v1.pdf'} +page_content='5 1 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9FKT4oBgHgl3EQfaS5z/content/2301.11807v1.pdf'} +page_content='5 2 −100 −80 −60 −40 −20 0 20 40 60 x+ GF/(qm 2 β)1/4 C= 0 C= 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9FKT4oBgHgl3EQfaS5z/content/2301.11807v1.pdf'} +page_content='1 C= 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9FKT4oBgHgl3EQfaS5z/content/2301.11807v1.pdf'} +page_content='2 Figure 9: The plot of the function GF/(√qmβ1/4 vs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9FKT4oBgHgl3EQfaS5z/content/2301.11807v1.pdf'} +page_content=' x+).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9FKT4oBgHgl3EQfaS5z/content/2301.11807v1.pdf'} +page_content=' The dashed curve corresponds to C = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9FKT4oBgHgl3EQfaS5z/content/2301.11807v1.pdf'} +page_content='1, the solid curve is for C = 0, and the dashed-doted curve corresponds to C = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9FKT4oBgHgl3EQfaS5z/content/2301.11807v1.pdf'} +page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9FKT4oBgHgl3EQfaS5z/content/2301.11807v1.pdf'} +page_content=' [9] S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9FKT4oBgHgl3EQfaS5z/content/2301.11807v1.pdf'} +page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9FKT4oBgHgl3EQfaS5z/content/2301.11807v1.pdf'} +page_content=' Hartnoll and P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9FKT4oBgHgl3EQfaS5z/content/2301.11807v1.pdf'} +page_content=' Kovtun, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9FKT4oBgHgl3EQfaS5z/content/2301.11807v1.pdf'} +page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9FKT4oBgHgl3EQfaS5z/content/2301.11807v1.pdf'} +page_content=' D 76, 066001 (2007).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9FKT4oBgHgl3EQfaS5z/content/2301.11807v1.pdf'} +page_content=' [10] S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9FKT4oBgHgl3EQfaS5z/content/2301.11807v1.pdf'} +page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9FKT4oBgHgl3EQfaS5z/content/2301.11807v1.pdf'} +page_content=' Hartnoll, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9FKT4oBgHgl3EQfaS5z/content/2301.11807v1.pdf'} +page_content=' K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9FKT4oBgHgl3EQfaS5z/content/2301.11807v1.pdf'} +page_content=' Kovtun , M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9FKT4oBgHgl3EQfaS5z/content/2301.11807v1.pdf'} +page_content=' Muller, and S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9FKT4oBgHgl3EQfaS5z/content/2301.11807v1.pdf'} +page_content=' Sachdev, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9FKT4oBgHgl3EQfaS5z/content/2301.11807v1.pdf'} +page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9FKT4oBgHgl3EQfaS5z/content/2301.11807v1.pdf'} +page_content=' B 76, 144502 (2007).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9FKT4oBgHgl3EQfaS5z/content/2301.11807v1.pdf'} +page_content=' [11] S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9FKT4oBgHgl3EQfaS5z/content/2301.11807v1.pdf'} +page_content=' Dutta, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9FKT4oBgHgl3EQfaS5z/content/2301.11807v1.pdf'} +page_content=' Jain, and R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9FKT4oBgHgl3EQfaS5z/content/2301.11807v1.pdf'} +page_content=' Soni, JHEP 1312, 060 (2013).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9FKT4oBgHgl3EQfaS5z/content/2301.11807v1.pdf'} +page_content=' [12] S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9FKT4oBgHgl3EQfaS5z/content/2301.11807v1.pdf'} +page_content=' I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9FKT4oBgHgl3EQfaS5z/content/2301.11807v1.pdf'} +page_content=' Kruglov, Ann.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9FKT4oBgHgl3EQfaS5z/content/2301.11807v1.pdf'} +page_content=' Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9FKT4oBgHgl3EQfaS5z/content/2301.11807v1.pdf'} +page_content=' 353, 299 (2015).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9FKT4oBgHgl3EQfaS5z/content/2301.11807v1.pdf'} +page_content=' [13] M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9FKT4oBgHgl3EQfaS5z/content/2301.11807v1.pdf'} +page_content=' Born and L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9FKT4oBgHgl3EQfaS5z/content/2301.11807v1.pdf'} +page_content=' Infeld, Proc.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9FKT4oBgHgl3EQfaS5z/content/2301.11807v1.pdf'} +page_content=' R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9FKT4oBgHgl3EQfaS5z/content/2301.11807v1.pdf'} +page_content=' Soc.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9FKT4oBgHgl3EQfaS5z/content/2301.11807v1.pdf'} +page_content=' Lond.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9FKT4oBgHgl3EQfaS5z/content/2301.11807v1.pdf'} +page_content=' 144, 425 (1934).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9FKT4oBgHgl3EQfaS5z/content/2301.11807v1.pdf'} +page_content=' [14] W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9FKT4oBgHgl3EQfaS5z/content/2301.11807v1.pdf'} +page_content=' Heisenberg and H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9FKT4oBgHgl3EQfaS5z/content/2301.11807v1.pdf'} +page_content=' Euler, Z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9FKT4oBgHgl3EQfaS5z/content/2301.11807v1.pdf'} +page_content=' Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9FKT4oBgHgl3EQfaS5z/content/2301.11807v1.pdf'} +page_content=' 98, 714 (1936).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9FKT4oBgHgl3EQfaS5z/content/2301.11807v1.pdf'} +page_content=' [15] H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9FKT4oBgHgl3EQfaS5z/content/2301.11807v1.pdf'} +page_content=' H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9FKT4oBgHgl3EQfaS5z/content/2301.11807v1.pdf'} +page_content=' Soleng, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9FKT4oBgHgl3EQfaS5z/content/2301.11807v1.pdf'} +page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9FKT4oBgHgl3EQfaS5z/content/2301.11807v1.pdf'} +page_content=' D 52, 6178 (1995).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9FKT4oBgHgl3EQfaS5z/content/2301.11807v1.pdf'} +page_content=' [16] D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9FKT4oBgHgl3EQfaS5z/content/2301.11807v1.pdf'} +page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9FKT4oBgHgl3EQfaS5z/content/2301.11807v1.pdf'} +page_content=' Gitman and A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9FKT4oBgHgl3EQfaS5z/content/2301.11807v1.pdf'} +page_content=' E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9FKT4oBgHgl3EQfaS5z/content/2301.11807v1.pdf'} +page_content=' Shabad, Eur.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9FKT4oBgHgl3EQfaS5z/content/2301.11807v1.pdf'} +page_content=' Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9FKT4oBgHgl3EQfaS5z/content/2301.11807v1.pdf'} +page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9FKT4oBgHgl3EQfaS5z/content/2301.11807v1.pdf'} +page_content=' C 74, 3186 (2014).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9FKT4oBgHgl3EQfaS5z/content/2301.11807v1.pdf'} +page_content=' [17] C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9FKT4oBgHgl3EQfaS5z/content/2301.11807v1.pdf'} +page_content=' V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9FKT4oBgHgl3EQfaS5z/content/2301.11807v1.pdf'} +page_content=' Costa, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9FKT4oBgHgl3EQfaS5z/content/2301.11807v1.pdf'} +page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9FKT4oBgHgl3EQfaS5z/content/2301.11807v1.pdf'} +page_content=' Gitman, and A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9FKT4oBgHgl3EQfaS5z/content/2301.11807v1.pdf'} +page_content=' E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9FKT4oBgHgl3EQfaS5z/content/2301.11807v1.pdf'} +page_content=' Shabad, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9FKT4oBgHgl3EQfaS5z/content/2301.11807v1.pdf'} +page_content=' Scripta 90, 074012 (2015).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9FKT4oBgHgl3EQfaS5z/content/2301.11807v1.pdf'} +page_content=' [18] S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9FKT4oBgHgl3EQfaS5z/content/2301.11807v1.pdf'} +page_content=' I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9FKT4oBgHgl3EQfaS5z/content/2301.11807v1.pdf'} +page_content=' Kruglov, Commun.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9FKT4oBgHgl3EQfaS5z/content/2301.11807v1.pdf'} +page_content=' Theor.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9FKT4oBgHgl3EQfaS5z/content/2301.11807v1.pdf'} +page_content=' Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9FKT4oBgHgl3EQfaS5z/content/2301.11807v1.pdf'} +page_content=' 66, 59 (2016).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9FKT4oBgHgl3EQfaS5z/content/2301.11807v1.pdf'} +page_content=' [19] S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9FKT4oBgHgl3EQfaS5z/content/2301.11807v1.pdf'} +page_content=' I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9FKT4oBgHgl3EQfaS5z/content/2301.11807v1.pdf'} +page_content=' Kruglov, Mod.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9FKT4oBgHgl3EQfaS5z/content/2301.11807v1.pdf'} +page_content=' Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9FKT4oBgHgl3EQfaS5z/content/2301.11807v1.pdf'} +page_content=' Lett.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9FKT4oBgHgl3EQfaS5z/content/2301.11807v1.pdf'} +page_content=' A 32, 1750201 (2017).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9FKT4oBgHgl3EQfaS5z/content/2301.11807v1.pdf'} +page_content=' [20] R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9FKT4oBgHgl3EQfaS5z/content/2301.11807v1.pdf'} +page_content=' Pellicer and R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9FKT4oBgHgl3EQfaS5z/content/2301.11807v1.pdf'} +page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9FKT4oBgHgl3EQfaS5z/content/2301.11807v1.pdf'} +page_content=' Torrence, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9FKT4oBgHgl3EQfaS5z/content/2301.11807v1.pdf'} +page_content=' Math.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9FKT4oBgHgl3EQfaS5z/content/2301.11807v1.pdf'} +page_content=' Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9FKT4oBgHgl3EQfaS5z/content/2301.11807v1.pdf'} +page_content=' 10, 1718 (1969).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9FKT4oBgHgl3EQfaS5z/content/2301.11807v1.pdf'} +page_content=' [21] H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9FKT4oBgHgl3EQfaS5z/content/2301.11807v1.pdf'} +page_content=' P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9FKT4oBgHgl3EQfaS5z/content/2301.11807v1.pdf'} +page_content=' de Oliveira, Class.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9FKT4oBgHgl3EQfaS5z/content/2301.11807v1.pdf'} +page_content=' Quant.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9FKT4oBgHgl3EQfaS5z/content/2301.11807v1.pdf'} +page_content=' Grav.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9FKT4oBgHgl3EQfaS5z/content/2301.11807v1.pdf'} +page_content=' 11, 1469 (1994).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9FKT4oBgHgl3EQfaS5z/content/2301.11807v1.pdf'} +page_content=' 13 [22] E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9FKT4oBgHgl3EQfaS5z/content/2301.11807v1.pdf'} +page_content=' Ay´on-Beato and A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9FKT4oBgHgl3EQfaS5z/content/2301.11807v1.pdf'} +page_content=' Gar´cia, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9FKT4oBgHgl3EQfaS5z/content/2301.11807v1.pdf'} +page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9FKT4oBgHgl3EQfaS5z/content/2301.11807v1.pdf'} +page_content=' Lett.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9FKT4oBgHgl3EQfaS5z/content/2301.11807v1.pdf'} +page_content=' 80, 5056 (1998).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9FKT4oBgHgl3EQfaS5z/content/2301.11807v1.pdf'} +page_content=' [23] K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9FKT4oBgHgl3EQfaS5z/content/2301.11807v1.pdf'} +page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9FKT4oBgHgl3EQfaS5z/content/2301.11807v1.pdf'} +page_content=' Bronnikov, V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9FKT4oBgHgl3EQfaS5z/content/2301.11807v1.pdf'} +page_content=' N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9FKT4oBgHgl3EQfaS5z/content/2301.11807v1.pdf'} +page_content=' Melnikov, G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9FKT4oBgHgl3EQfaS5z/content/2301.11807v1.pdf'} +page_content=' N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9FKT4oBgHgl3EQfaS5z/content/2301.11807v1.pdf'} +page_content=' Shikin, and K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9FKT4oBgHgl3EQfaS5z/content/2301.11807v1.pdf'} +page_content=' P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9FKT4oBgHgl3EQfaS5z/content/2301.11807v1.pdf'} +page_content=' Staniukovich, Ann.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9FKT4oBgHgl3EQfaS5z/content/2301.11807v1.pdf'} +page_content=' Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9FKT4oBgHgl3EQfaS5z/content/2301.11807v1.pdf'} +page_content=' 118, 84 (1979).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9FKT4oBgHgl3EQfaS5z/content/2301.11807v1.pdf'} +page_content=' [24] K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9FKT4oBgHgl3EQfaS5z/content/2301.11807v1.pdf'} +page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9FKT4oBgHgl3EQfaS5z/content/2301.11807v1.pdf'} +page_content=' Bronnikov, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9FKT4oBgHgl3EQfaS5z/content/2301.11807v1.pdf'} +page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9FKT4oBgHgl3EQfaS5z/content/2301.11807v1.pdf'} +page_content=' D 63, 044005 (2001).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9FKT4oBgHgl3EQfaS5z/content/2301.11807v1.pdf'} +page_content=' [25] K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9FKT4oBgHgl3EQfaS5z/content/2301.11807v1.pdf'} +page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9FKT4oBgHgl3EQfaS5z/content/2301.11807v1.pdf'} +page_content=' Bronnikov, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9FKT4oBgHgl3EQfaS5z/content/2301.11807v1.pdf'} +page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9FKT4oBgHgl3EQfaS5z/content/2301.11807v1.pdf'} +page_content=' Lett.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9FKT4oBgHgl3EQfaS5z/content/2301.11807v1.pdf'} +page_content=' 85, 4641 (2000).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9FKT4oBgHgl3EQfaS5z/content/2301.11807v1.pdf'} +page_content=' [26] K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9FKT4oBgHgl3EQfaS5z/content/2301.11807v1.pdf'} +page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9FKT4oBgHgl3EQfaS5z/content/2301.11807v1.pdf'} +page_content=' Bronnikov, G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9FKT4oBgHgl3EQfaS5z/content/2301.11807v1.pdf'} +page_content=' N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9FKT4oBgHgl3EQfaS5z/content/2301.11807v1.pdf'} +page_content=' Shikin, and E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9FKT4oBgHgl3EQfaS5z/content/2301.11807v1.pdf'} +page_content=' N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9FKT4oBgHgl3EQfaS5z/content/2301.11807v1.pdf'} +page_content=' Sibileva, Grav.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9FKT4oBgHgl3EQfaS5z/content/2301.11807v1.pdf'} +page_content=' Cosmol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9FKT4oBgHgl3EQfaS5z/content/2301.11807v1.pdf'} +page_content=' 9, 169 (2003).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9FKT4oBgHgl3EQfaS5z/content/2301.11807v1.pdf'} +page_content=' [27] A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9FKT4oBgHgl3EQfaS5z/content/2301.11807v1.pdf'} +page_content=' Burinskii and S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9FKT4oBgHgl3EQfaS5z/content/2301.11807v1.pdf'} +page_content=' R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9FKT4oBgHgl3EQfaS5z/content/2301.11807v1.pdf'} +page_content=' Hildebrandt, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9FKT4oBgHgl3EQfaS5z/content/2301.11807v1.pdf'} +page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9FKT4oBgHgl3EQfaS5z/content/2301.11807v1.pdf'} +page_content=' D 65, 104017 (2002).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9FKT4oBgHgl3EQfaS5z/content/2301.11807v1.pdf'} +page_content=' [28] J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9FKT4oBgHgl3EQfaS5z/content/2301.11807v1.pdf'} +page_content=' Diaz-Alonso and D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9FKT4oBgHgl3EQfaS5z/content/2301.11807v1.pdf'} +page_content=' Rubiera-Garcia, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9FKT4oBgHgl3EQfaS5z/content/2301.11807v1.pdf'} +page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9FKT4oBgHgl3EQfaS5z/content/2301.11807v1.pdf'} +page_content=' D 81, 064021 (2010).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9FKT4oBgHgl3EQfaS5z/content/2301.11807v1.pdf'} +page_content=' [29] N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9FKT4oBgHgl3EQfaS5z/content/2301.11807v1.pdf'} +page_content=' Breton, Gen.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9FKT4oBgHgl3EQfaS5z/content/2301.11807v1.pdf'} +page_content=' Rel.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9FKT4oBgHgl3EQfaS5z/content/2301.11807v1.pdf'} +page_content=' Grav.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9FKT4oBgHgl3EQfaS5z/content/2301.11807v1.pdf'} +page_content=' 37, 643 (2005).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9FKT4oBgHgl3EQfaS5z/content/2301.11807v1.pdf'} +page_content=' [30] M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9FKT4oBgHgl3EQfaS5z/content/2301.11807v1.pdf'} +page_content=' Novello, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9FKT4oBgHgl3EQfaS5z/content/2301.11807v1.pdf'} +page_content=' E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9FKT4oBgHgl3EQfaS5z/content/2301.11807v1.pdf'} +page_content=' Perez Bergliaffa, and J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9FKT4oBgHgl3EQfaS5z/content/2301.11807v1.pdf'} +page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9FKT4oBgHgl3EQfaS5z/content/2301.11807v1.pdf'} +page_content=' Salim, Class.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9FKT4oBgHgl3EQfaS5z/content/2301.11807v1.pdf'} +page_content=' Quant.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9FKT4oBgHgl3EQfaS5z/content/2301.11807v1.pdf'} +page_content=' Grav.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9FKT4oBgHgl3EQfaS5z/content/2301.11807v1.pdf'} +page_content=' 17, 3821 (2000).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9FKT4oBgHgl3EQfaS5z/content/2301.11807v1.pdf'} +page_content=' [31] R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9FKT4oBgHgl3EQfaS5z/content/2301.11807v1.pdf'} +page_content=' Garcia-Salcedo, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9FKT4oBgHgl3EQfaS5z/content/2301.11807v1.pdf'} +page_content=' Gonzalez, and I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9FKT4oBgHgl3EQfaS5z/content/2301.11807v1.pdf'} +page_content=' Quiros, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9FKT4oBgHgl3EQfaS5z/content/2301.11807v1.pdf'} +page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9FKT4oBgHgl3EQfaS5z/content/2301.11807v1.pdf'} +page_content=' D 89, 084047 (2014).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9FKT4oBgHgl3EQfaS5z/content/2301.11807v1.pdf'} +page_content=' [32] J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9FKT4oBgHgl3EQfaS5z/content/2301.11807v1.pdf'} +page_content=' P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9FKT4oBgHgl3EQfaS5z/content/2301.11807v1.pdf'} +page_content=' S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9FKT4oBgHgl3EQfaS5z/content/2301.11807v1.pdf'} +page_content=' Lemos and V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9FKT4oBgHgl3EQfaS5z/content/2301.11807v1.pdf'} +page_content=' T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9FKT4oBgHgl3EQfaS5z/content/2301.11807v1.pdf'} +page_content=' Zanchin, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9FKT4oBgHgl3EQfaS5z/content/2301.11807v1.pdf'} +page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9FKT4oBgHgl3EQfaS5z/content/2301.11807v1.pdf'} +page_content=' D 83, 124005 (2011).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9FKT4oBgHgl3EQfaS5z/content/2301.11807v1.pdf'} +page_content=' [33] L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9FKT4oBgHgl3EQfaS5z/content/2301.11807v1.pdf'} +page_content=' Balart and E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9FKT4oBgHgl3EQfaS5z/content/2301.11807v1.pdf'} +page_content=' C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9FKT4oBgHgl3EQfaS5z/content/2301.11807v1.pdf'} +page_content=' Vagenas, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9FKT4oBgHgl3EQfaS5z/content/2301.11807v1.pdf'} +page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9FKT4oBgHgl3EQfaS5z/content/2301.11807v1.pdf'} +page_content=' D 90, 124045 (2014).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9FKT4oBgHgl3EQfaS5z/content/2301.11807v1.pdf'} +page_content=' [34] S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9FKT4oBgHgl3EQfaS5z/content/2301.11807v1.pdf'} +page_content=' I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9FKT4oBgHgl3EQfaS5z/content/2301.11807v1.pdf'} +page_content=' Kruglov, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9FKT4oBgHgl3EQfaS5z/content/2301.11807v1.pdf'} +page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9FKT4oBgHgl3EQfaS5z/content/2301.11807v1.pdf'} +page_content=' D 94, 044026 (2016).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9FKT4oBgHgl3EQfaS5z/content/2301.11807v1.pdf'} +page_content=' [35] S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9FKT4oBgHgl3EQfaS5z/content/2301.11807v1.pdf'} +page_content=' I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9FKT4oBgHgl3EQfaS5z/content/2301.11807v1.pdf'} +page_content=' Kruglov, Ann.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9FKT4oBgHgl3EQfaS5z/content/2301.11807v1.pdf'} +page_content=' Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9FKT4oBgHgl3EQfaS5z/content/2301.11807v1.pdf'} +page_content=' (Berlin) 528, 588 (2016).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9FKT4oBgHgl3EQfaS5z/content/2301.11807v1.pdf'} +page_content=' [36] H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9FKT4oBgHgl3EQfaS5z/content/2301.11807v1.pdf'} +page_content=' Yajima and T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9FKT4oBgHgl3EQfaS5z/content/2301.11807v1.pdf'} +page_content=' Tamaki, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9FKT4oBgHgl3EQfaS5z/content/2301.11807v1.pdf'} +page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9FKT4oBgHgl3EQfaS5z/content/2301.11807v1.pdf'} +page_content=' D 63, 064007 (2001).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9FKT4oBgHgl3EQfaS5z/content/2301.11807v1.pdf'} +page_content=' [37] K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9FKT4oBgHgl3EQfaS5z/content/2301.11807v1.pdf'} +page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9FKT4oBgHgl3EQfaS5z/content/2301.11807v1.pdf'} +page_content=' Bronnikov, Grav.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9FKT4oBgHgl3EQfaS5z/content/2301.11807v1.pdf'} +page_content=' Cosmol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9FKT4oBgHgl3EQfaS5z/content/2301.11807v1.pdf'} +page_content=' 23, 343 (2017).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9FKT4oBgHgl3EQfaS5z/content/2301.11807v1.pdf'} +page_content=' [38] K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9FKT4oBgHgl3EQfaS5z/content/2301.11807v1.pdf'} +page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9FKT4oBgHgl3EQfaS5z/content/2301.11807v1.pdf'} +page_content=' Bronnikov, Int.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9FKT4oBgHgl3EQfaS5z/content/2301.11807v1.pdf'} +page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9FKT4oBgHgl3EQfaS5z/content/2301.11807v1.pdf'} +page_content=' Mod.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9FKT4oBgHgl3EQfaS5z/content/2301.11807v1.pdf'} +page_content=' Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9FKT4oBgHgl3EQfaS5z/content/2301.11807v1.pdf'} +page_content=' D 27, 1841005 (2018).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9FKT4oBgHgl3EQfaS5z/content/2301.11807v1.pdf'} +page_content=' [39] S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9FKT4oBgHgl3EQfaS5z/content/2301.11807v1.pdf'} +page_content=' I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9FKT4oBgHgl3EQfaS5z/content/2301.11807v1.pdf'} +page_content=' Kruglov, Int.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9FKT4oBgHgl3EQfaS5z/content/2301.11807v1.pdf'} +page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9FKT4oBgHgl3EQfaS5z/content/2301.11807v1.pdf'} +page_content=' Mod.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9FKT4oBgHgl3EQfaS5z/content/2301.11807v1.pdf'} +page_content=' Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9FKT4oBgHgl3EQfaS5z/content/2301.11807v1.pdf'} +page_content=' A 33, 1850023 (2018).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9FKT4oBgHgl3EQfaS5z/content/2301.11807v1.pdf'} +page_content=' [40] S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9FKT4oBgHgl3EQfaS5z/content/2301.11807v1.pdf'} +page_content=' I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9FKT4oBgHgl3EQfaS5z/content/2301.11807v1.pdf'} +page_content=' Kruglov, Ann.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9FKT4oBgHgl3EQfaS5z/content/2301.11807v1.pdf'} +page_content=' Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9FKT4oBgHgl3EQfaS5z/content/2301.11807v1.pdf'} +page_content=' 383, 550 (2017).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9FKT4oBgHgl3EQfaS5z/content/2301.11807v1.pdf'} +page_content=' [41] R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9FKT4oBgHgl3EQfaS5z/content/2301.11807v1.pdf'} +page_content=' Garc´ıa-Salcedo and N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9FKT4oBgHgl3EQfaS5z/content/2301.11807v1.pdf'} +page_content=' Breton, Int.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9FKT4oBgHgl3EQfaS5z/content/2301.11807v1.pdf'} +page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9FKT4oBgHgl3EQfaS5z/content/2301.11807v1.pdf'} +page_content=' Mod.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9FKT4oBgHgl3EQfaS5z/content/2301.11807v1.pdf'} +page_content=' Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9FKT4oBgHgl3EQfaS5z/content/2301.11807v1.pdf'} +page_content=' A 15, 4341 (2000).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9FKT4oBgHgl3EQfaS5z/content/2301.11807v1.pdf'} +page_content=' 14 [42] C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9FKT4oBgHgl3EQfaS5z/content/2301.11807v1.pdf'} +page_content=' S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9FKT4oBgHgl3EQfaS5z/content/2301.11807v1.pdf'} +page_content=' Camara, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9FKT4oBgHgl3EQfaS5z/content/2301.11807v1.pdf'} +page_content=' R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9FKT4oBgHgl3EQfaS5z/content/2301.11807v1.pdf'} +page_content=' de Garcia Maia, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9FKT4oBgHgl3EQfaS5z/content/2301.11807v1.pdf'} +page_content=' C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9FKT4oBgHgl3EQfaS5z/content/2301.11807v1.pdf'} +page_content=' Carvalho, and J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9FKT4oBgHgl3EQfaS5z/content/2301.11807v1.pdf'} +page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9FKT4oBgHgl3EQfaS5z/content/2301.11807v1.pdf'} +page_content=' S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9FKT4oBgHgl3EQfaS5z/content/2301.11807v1.pdf'} +page_content=' Lima, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9FKT4oBgHgl3EQfaS5z/content/2301.11807v1.pdf'} +page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9FKT4oBgHgl3EQfaS5z/content/2301.11807v1.pdf'} +page_content=' D 69, 123504 (2004).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9FKT4oBgHgl3EQfaS5z/content/2301.11807v1.pdf'} +page_content=' [43] E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9FKT4oBgHgl3EQfaS5z/content/2301.11807v1.pdf'} +page_content=' Elizalde, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9FKT4oBgHgl3EQfaS5z/content/2301.11807v1.pdf'} +page_content=' E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9FKT4oBgHgl3EQfaS5z/content/2301.11807v1.pdf'} +page_content=' Lidsey, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9FKT4oBgHgl3EQfaS5z/content/2301.11807v1.pdf'} +page_content=' Nojiri, and S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9FKT4oBgHgl3EQfaS5z/content/2301.11807v1.pdf'} +page_content=' D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9FKT4oBgHgl3EQfaS5z/content/2301.11807v1.pdf'} +page_content=' Odintsov, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9FKT4oBgHgl3EQfaS5z/content/2301.11807v1.pdf'} +page_content=' Lett.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9FKT4oBgHgl3EQfaS5z/content/2301.11807v1.pdf'} +page_content=' B 574, 1 (2003).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9FKT4oBgHgl3EQfaS5z/content/2301.11807v1.pdf'} +page_content=' [44] M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9FKT4oBgHgl3EQfaS5z/content/2301.11807v1.pdf'} +page_content=' Novello, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9FKT4oBgHgl3EQfaS5z/content/2301.11807v1.pdf'} +page_content=' E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9FKT4oBgHgl3EQfaS5z/content/2301.11807v1.pdf'} +page_content=' Perez Bergliaffa, and J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9FKT4oBgHgl3EQfaS5z/content/2301.11807v1.pdf'} +page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9FKT4oBgHgl3EQfaS5z/content/2301.11807v1.pdf'} +page_content=' Salim, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9FKT4oBgHgl3EQfaS5z/content/2301.11807v1.pdf'} +page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9FKT4oBgHgl3EQfaS5z/content/2301.11807v1.pdf'} +page_content=' D 69, 127301 (2004).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9FKT4oBgHgl3EQfaS5z/content/2301.11807v1.pdf'} +page_content=' [45] M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9FKT4oBgHgl3EQfaS5z/content/2301.11807v1.pdf'} +page_content=' Novello, E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9FKT4oBgHgl3EQfaS5z/content/2301.11807v1.pdf'} +page_content=' Goulart, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9FKT4oBgHgl3EQfaS5z/content/2301.11807v1.pdf'} +page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9FKT4oBgHgl3EQfaS5z/content/2301.11807v1.pdf'} +page_content=' Salim, and S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9FKT4oBgHgl3EQfaS5z/content/2301.11807v1.pdf'} +page_content=' E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9FKT4oBgHgl3EQfaS5z/content/2301.11807v1.pdf'} +page_content=' Perez Bergliaffa, Class.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9FKT4oBgHgl3EQfaS5z/content/2301.11807v1.pdf'} +page_content=' Quant.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9FKT4oBgHgl3EQfaS5z/content/2301.11807v1.pdf'} +page_content=' Grav.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9FKT4oBgHgl3EQfaS5z/content/2301.11807v1.pdf'} +page_content=' 24, 3021 (2007).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9FKT4oBgHgl3EQfaS5z/content/2301.11807v1.pdf'} +page_content=' [46] D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9FKT4oBgHgl3EQfaS5z/content/2301.11807v1.pdf'} +page_content=' N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9FKT4oBgHgl3EQfaS5z/content/2301.11807v1.pdf'} +page_content=' Vollick, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9FKT4oBgHgl3EQfaS5z/content/2301.11807v1.pdf'} +page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9FKT4oBgHgl3EQfaS5z/content/2301.11807v1.pdf'} +page_content=' D 78, 063524 (2008).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9FKT4oBgHgl3EQfaS5z/content/2301.11807v1.pdf'} +page_content=' [47] S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9FKT4oBgHgl3EQfaS5z/content/2301.11807v1.pdf'} +page_content=' I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9FKT4oBgHgl3EQfaS5z/content/2301.11807v1.pdf'} +page_content=' Kruglov, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9FKT4oBgHgl3EQfaS5z/content/2301.11807v1.pdf'} +page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9FKT4oBgHgl3EQfaS5z/content/2301.11807v1.pdf'} +page_content=' D 92, 123523 (2015).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9FKT4oBgHgl3EQfaS5z/content/2301.11807v1.pdf'} +page_content=' [48] S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9FKT4oBgHgl3EQfaS5z/content/2301.11807v1.pdf'} +page_content=' I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9FKT4oBgHgl3EQfaS5z/content/2301.11807v1.pdf'} +page_content=' Kruglov, Int.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9FKT4oBgHgl3EQfaS5z/content/2301.11807v1.pdf'} +page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9FKT4oBgHgl3EQfaS5z/content/2301.11807v1.pdf'} +page_content=' Mod.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9FKT4oBgHgl3EQfaS5z/content/2301.11807v1.pdf'} +page_content=' Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9FKT4oBgHgl3EQfaS5z/content/2301.11807v1.pdf'} +page_content=' A 32, 1750071 (2017).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9FKT4oBgHgl3EQfaS5z/content/2301.11807v1.pdf'} +page_content=' [49] S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9FKT4oBgHgl3EQfaS5z/content/2301.11807v1.pdf'} +page_content=' I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9FKT4oBgHgl3EQfaS5z/content/2301.11807v1.pdf'} +page_content=' Kruglov, Int.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9FKT4oBgHgl3EQfaS5z/content/2301.11807v1.pdf'} +page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9FKT4oBgHgl3EQfaS5z/content/2301.11807v1.pdf'} +page_content=' Mod.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9FKT4oBgHgl3EQfaS5z/content/2301.11807v1.pdf'} +page_content=' Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9FKT4oBgHgl3EQfaS5z/content/2301.11807v1.pdf'} +page_content=' D 25, 1640002 (2016).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9FKT4oBgHgl3EQfaS5z/content/2301.11807v1.pdf'} +page_content=' [50] A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9FKT4oBgHgl3EQfaS5z/content/2301.11807v1.pdf'} +page_content=' E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9FKT4oBgHgl3EQfaS5z/content/2301.11807v1.pdf'} +page_content=' Shabad and V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9FKT4oBgHgl3EQfaS5z/content/2301.11807v1.pdf'} +page_content=' V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9FKT4oBgHgl3EQfaS5z/content/2301.11807v1.pdf'} +page_content=' Usov, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9FKT4oBgHgl3EQfaS5z/content/2301.11807v1.pdf'} +page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9FKT4oBgHgl3EQfaS5z/content/2301.11807v1.pdf'} +page_content=' D 83, 105006 (2011).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9FKT4oBgHgl3EQfaS5z/content/2301.11807v1.pdf'} +page_content='5).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9FKT4oBgHgl3EQfaS5z/content/2301.11807v1.pdf'} +page_content=' [51] S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9FKT4oBgHgl3EQfaS5z/content/2301.11807v1.pdf'} +page_content=' W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9FKT4oBgHgl3EQfaS5z/content/2301.11807v1.pdf'} +page_content=' Hawking and D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9FKT4oBgHgl3EQfaS5z/content/2301.11807v1.pdf'} +page_content=' N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9FKT4oBgHgl3EQfaS5z/content/2301.11807v1.pdf'} +page_content=' Page, Commun.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9FKT4oBgHgl3EQfaS5z/content/2301.11807v1.pdf'} +page_content=' Math.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9FKT4oBgHgl3EQfaS5z/content/2301.11807v1.pdf'} +page_content=' Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9FKT4oBgHgl3EQfaS5z/content/2301.11807v1.pdf'} +page_content=' 87, 577 (1983).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9FKT4oBgHgl3EQfaS5z/content/2301.11807v1.pdf'} +page_content=' [52] J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9FKT4oBgHgl3EQfaS5z/content/2301.11807v1.pdf'} +page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9FKT4oBgHgl3EQfaS5z/content/2301.11807v1.pdf'} +page_content=' R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9FKT4oBgHgl3EQfaS5z/content/2301.11807v1.pdf'} +page_content=' Cembranos, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9FKT4oBgHgl3EQfaS5z/content/2301.11807v1.pdf'} +page_content=' Cruz-Dombriz, and J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9FKT4oBgHgl3EQfaS5z/content/2301.11807v1.pdf'} +page_content=' Jarillo, Universe, 1, 412 (2015).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9FKT4oBgHgl3EQfaS5z/content/2301.11807v1.pdf'} +page_content=' 15' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/E9FKT4oBgHgl3EQfaS5z/content/2301.11807v1.pdf'}