AdS黑洞热力学中的临界现象
发布时间：2018-11-03 06:44
【摘要】：黑洞热力学是人们近年来研究的热门课题之一。从上世纪七十年代发现黑洞具有热辐射及建立热力学定律以来,人们对黑洞热力学的研究已经取得了很大的进展。本文中,我们类比了范式模型和Anti-de Sitter(AdS)黑洞的物态方程,进而研究了F(R)引力中的AdS黑洞的相变和临界指数等黑洞热力学中的临界行为。 在第一章绪论中,我们主要是对黑洞模型的发展和黑洞热力学理论做一个综述。我们简单介绍了有关黑洞以及AdS黑洞的一些基本概念和性质,然后阐述了黑洞的Hawking辐射、黑洞热力学定律以及黑洞的相变等理论知识。 在第二章中,我们主要介绍了范氏气体与AdS黑洞之间热力学临界行为的相似性。首先,我们着重阐述了范式气体的物态方程及其气液相变中主要的临界性质。范式气体的一级相变点(临界点)终止于气液共存线的终点,其临界系数pc=PcVc/Tc=3/8,相应的临界指数为α=0,β=1/2,γ=1,δ=3。其次,类比了范式气体和AdS黑洞的物态方程,阐述了AdS黑洞的相变和临界指数等黑洞热力学中的临界行为与范氏气体的临界行为之间的相似性。 在第三章中,我们着重研究F(R)引力中常里奇曲率黑洞的热力学性质。我们把里奇曲率R0视为等效的宇宙常数和热力学压强,把其共轭量视为热力学体积,然后分析了该黑洞热力学中的临界行为和临界指数。我们发现F(R)影响了体系的吉布斯自由能和相变。在临界点的临界系数ρc随f(R)的导数f’(R0)的增大而增大。我们也发现该黑洞的临界指数并不依赖于本文所考虑的f(R)理论的形式,且和范氏气体中的一致。最后,我们对本文进行的工作经行了总结和展望。
[Abstract]:Black hole thermodynamics is one of the hot topics in recent years. Since the discovery of the thermal radiation of black holes and the establishment of thermodynamic laws in the 1970s, great progress has been made in the study of the thermodynamics of black holes. In this paper, we compare the normal form model with the equation of state of Anti-de Sitter (AdS) black hole, and then study the phase transition of AdS black hole in F (R) gravity and the critical behavior of black hole thermodynamics such as critical exponent. In the first chapter, we review the development of black hole model and the theory of black hole thermodynamics. We briefly introduce some basic concepts and properties of black holes and AdS black holes. Then we expound the Hawking radiation of black holes, the thermodynamic laws of black holes and the phase transition of black holes. In chapter 2, we mainly introduce the similarity of thermodynamic critical behavior between van der gas and AdS black hole. Firstly, we focus on the equation of state of normal form gas and the main critical properties of gas-liquid phase transition. The first-order phase transition point (critical point) of normal form gas terminates at the end of gas-liquid coexistence line. The critical exponent of the critical coefficient pc=PcVc/Tc=3/8, is 伪 = 0, 尾 = 1 / 2, 纬 = 1, 未 = 3. Secondly, by analogy with the equation of state of normal form gas and AdS black hole, the similarity between the critical behavior of AdS black hole in the thermodynamics of black hole such as phase transition and critical exponent of AdS black hole and the critical behavior of van's gas is discussed. In Chapter 3, we focus on the thermodynamic properties of a constant Ritchie curvature black hole in F (R) gravity. We regard Ritchie curvature R _ 0 as the equivalent cosmic constant and thermodynamic pressure, and regard its conjugate quantity as the thermodynamic volume. Then we analyze the critical behavior and critical exponent of the black hole thermodynamics. We find that F (R) affects the Gibbs free energy and phase transition of the system. The critical coefficient 蟻 c at the critical point increases with the increase of the derivative f'(R 0) of f (R). It is also found that the critical exponent of the black hole does not depend on the form of the f (R) theory considered in this paper and is consistent with that in the van's gas. Finally, we summarize and look forward to the work done in this paper.
【学位授予单位】：湖南师范大学
【学位级别】：硕士
【学位授予年份】：2014
【分类号】：P145.8;O414.1
本文编号：2306990
[Abstract]:Black hole thermodynamics is one of the hot topics in recent years. Since the discovery of the thermal radiation of black holes and the establishment of thermodynamic laws in the 1970s, great progress has been made in the study of the thermodynamics of black holes. In this paper, we compare the normal form model with the equation of state of Anti-de Sitter (AdS) black hole, and then study the phase transition of AdS black hole in F (R) gravity and the critical behavior of black hole thermodynamics such as critical exponent. In the first chapter, we review the development of black hole model and the theory of black hole thermodynamics. We briefly introduce some basic concepts and properties of black holes and AdS black holes. Then we expound the Hawking radiation of black holes, the thermodynamic laws of black holes and the phase transition of black holes. In chapter 2, we mainly introduce the similarity of thermodynamic critical behavior between van der gas and AdS black hole. Firstly, we focus on the equation of state of normal form gas and the main critical properties of gas-liquid phase transition. The first-order phase transition point (critical point) of normal form gas terminates at the end of gas-liquid coexistence line. The critical exponent of the critical coefficient pc=PcVc/Tc=3/8, is 伪 = 0, 尾 = 1 / 2, 纬 = 1, 未 = 3. Secondly, by analogy with the equation of state of normal form gas and AdS black hole, the similarity between the critical behavior of AdS black hole in the thermodynamics of black hole such as phase transition and critical exponent of AdS black hole and the critical behavior of van's gas is discussed. In Chapter 3, we focus on the thermodynamic properties of a constant Ritchie curvature black hole in F (R) gravity. We regard Ritchie curvature R _ 0 as the equivalent cosmic constant and thermodynamic pressure, and regard its conjugate quantity as the thermodynamic volume. Then we analyze the critical behavior and critical exponent of the black hole thermodynamics. We find that F (R) affects the Gibbs free energy and phase transition of the system. The critical coefficient 蟻 c at the critical point increases with the increase of the derivative f'(R 0) of f (R). It is also found that the critical exponent of the black hole does not depend on the form of the f (R) theory considered in this paper and is consistent with that in the van's gas. Finally, we summarize and look forward to the work done in this paper.
【学位授予单位】：湖南师范大学
【学位级别】：硕士
【学位授予年份】：2014
【分类号】：P145.8;O414.1
【参考文献】
相关期刊论文 前1条
1 钱凤仪;黑洞理论的回顾与置疑[J];吉林工学院学报(自然科学版);2002年01期
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