【摘要】：黑洞熱力學(xué)是人們近年來(lái)研究的熱門課題之一。從上世紀(jì)七十年代發(fā)現(xiàn)黑洞具有熱輻射及建立熱力學(xué)定律以來(lái),人們對(duì)黑洞熱力學(xué)的研究已經(jīng)取得了很大的進(jìn)展。本文中,我們類比了范式模型和Anti-de Sitter(AdS)黑洞的物態(tài)方程,進(jìn)而研究了F(R)引力中的AdS黑洞的相變和臨界指數(shù)等黑洞熱力學(xué)中的臨界行為。 在第一章緒論中,我們主要是對(duì)黑洞模型的發(fā)展和黑洞熱力學(xué)理論做一個(gè)綜述。我們簡(jiǎn)單介紹了有關(guān)黑洞以及AdS黑洞的一些基本概念和性質(zhì),然后闡述了黑洞的Hawking輻射、黑洞熱力學(xué)定律以及黑洞的相變等理論知識(shí)。 在第二章中,我們主要介紹了范氏氣體與AdS黑洞之間熱力學(xué)臨界行為的相似性。首先,我們著重闡述了范式氣體的物態(tài)方程及其氣液相變中主要的臨界性質(zhì)。范式氣體的一級(jí)相變點(diǎn)(臨界點(diǎn))終止于氣液共存線的終點(diǎn),其臨界系數(shù)pc=PcVc/Tc=3/8,相應(yīng)的臨界指數(shù)為α=0,β=1/2,γ=1,δ=3。其次,類比了范式氣體和AdS黑洞的物態(tài)方程,闡述了AdS黑洞的相變和臨界指數(shù)等黑洞熱力學(xué)中的臨界行為與范氏氣體的臨界行為之間的相似性。 在第三章中,我們著重研究F(R)引力中常里奇曲率黑洞的熱力學(xué)性質(zhì)。我們把里奇曲率R0視為等效的宇宙常數(shù)和熱力學(xué)壓強(qiáng),把其共軛量視為熱力學(xué)體積,然后分析了該黑洞熱力學(xué)中的臨界行為和臨界指數(shù)。我們發(fā)現(xiàn)F(R)影響了體系的吉布斯自由能和相變。在臨界點(diǎn)的臨界系數(shù)ρc隨f(R)的導(dǎo)數(shù)f’(R0)的增大而增大。我們也發(fā)現(xiàn)該黑洞的臨界指數(shù)并不依賴于本文所考慮的f(R)理論的形式,且和范氏氣體中的一致。最后,我們對(duì)本文進(jìn)行的工作經(jīng)行了總結(jié)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 偽 = 0, 尾 = 1 / 2, 緯 = 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.
【學(xué)位授予單位】：湖南師范大學(xué)
【學(xué)位級(jí)別】：碩士
【學(xué)位授予年份】：2014
【分類號(hào)】：P145.8;O414.1

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相關(guān)期刊論文 前1條

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本文編號(hào)：2306990