黑洞热力学相变及其动力学对应

发布时间：2018-01-11 22:03

本文关键词：黑洞热力学相变及其动力学对应　出处：《上海交通大学》2015年博士论文　论文类型：学位论文

【摘要】：在本学位论文里,我们研究了几种黑洞模型的热力学性质以及动力学对应。主要内容包括：a)在扩展相空间里研究了Born-Infeld Anti-de Sitter(BI-AdS)黑洞和Gauss-Bonnet AdS(GB-AdS)黑洞的类范德瓦尔斯相变；b)研究了四维Reissner-Nordstrom Anti-de Sitter(RN-AdS)里洞的类范德瓦尔斯相变在动力学上的对应； c)构造了新的带毛转动黑洞解,并研究了该黑洞的热力学性质及其动力学对应。在给定的几种黑洞背景(BI-AdS黑洞和GB-AdS黑洞)中,我们把宇宙学常数A看成是一个变量,得到了所谓的扩展相空间。在这个新的相空间里,可以把黑洞的温度表达式改写成一个与范德瓦尔斯气液体系状态方程类似的新状态方程。对于BI-AdS黑洞模型中,新的“大黑洞—小黑洞——大黑洞”相变出现在四维时空中,而高维时空中只存在类范德瓦尔斯大黑洞和小黑洞相变,但是三维时空中的BI-AdS黑洞都没有发生这些相变。在巨正则系综中的D维带电GB-AdS黑洞模型中,我们发现类范德瓦尔斯大黑洞和小黑洞相变只发生在五维的球形视界的GB-AdS里洞背景中,而且此时电势Φ必须满足0Φ(?)。当Gauss-Bonnet曲率项的系数趋近于零时,即退化为任意维的RN-AdS黑洞情形,我们发现不存在类范德瓦尔斯大黑洞和小黑洞相变。之后我们将着眼点放在研究黑洞的类范德瓦尔斯相变与动力学稳定性的对应性上。物理学家一直希望黑洞的热力学相变能够在黑洞周围动力学扰动的似正规模频率和震荡的衰减时间上得到反映。我们考察了黑洞类范德瓦尔斯相变过程中大黑洞相和小黑洞相在标量扰动下的似正规模频率。我们发现无论是在等压过程中还是在等温过程中,随黑洞视界半径的变化,似正规模频率在大黑洞相和小黑洞相中的行为差别非常大。这种在大黑洞和小黑洞中似正规模频率差别可以区分黑洞的热力学相。我们进一步分析了影响黑洞似正规模频率的因素,给出了导致似正规模频率变化的物理诱因。这个研究结果为黑洞热力学相变在黑洞动力学稳定性中的反映提供了一个新的例子。最后我们讨论了三维时空带标量毛的黑洞解。通过设定合适的标量势函数V(Φ),我们得到了新的带毛转动黑洞解。而且这个新解的热力学量满足黑洞热力学第一定律。接下来,通过在黑洞时空背景中加入一个电磁扰动,我们计算带标量毛的转动黑洞的电磁扰动最低阶频率,发现似正规模频率的虚部的变化特征正好与热力学稳定性相对应。这一结论同样适用于三维时空中的静态带毛黑洞解。
[Abstract]:In this thesis. We have studied the thermodynamic properties and dynamical correspondence of several black hole models. The main contents include: a). The black holes of Born-Infeld Anti-de sitterus BI-AdS and Gauss-Bonnet Ads are studied in extended phase space. The van der Waals phase transition of the GB-AdS) black hole; B) the kinetic correspondence of the van der Waals phase transition in a four-dimensional Reissner-Nordstrom Anti-de sittery-RN-AdS) hole is studied. C) A new solution of a hairy rotating black hole is constructed, and the thermodynamic properties of the black hole and its dynamical correspondence are studied. In the given black hole background, BI-AdS black hole and GB-AdS black hole). We take the cosmological constant A as a variable and obtain the so-called extended phase space in this new phase space. The expression of the temperature of the black hole can be changed into a new equation of state similar to the equation of state of the van der Waals gas-liquid system, for the BI-AdS black hole model. The new "big black hole-small black hole-big black hole" phase transition appears in the four-dimensional spacetime, while in the high-dimensional spacetime there are only Van der Waals black hole and small black hole phase transition. But none of the BI-AdS black holes in 3D spacetime have these phase transitions. In the D dimensional charged GB-AdS black hole model in the grand canonical ensemble. We find that the phase transitions of Van der Waals like black holes and small black holes only occur in the GB-AdS hole background of the five-dimensional spherical event horizon, and the electric potential 桅 must satisfy 0 桅? When the coefficient of the Gauss-Bonnet curvature term approaches 00:00, it degenerates into an arbitrary dimensional RN-AdS black hole case. We find that there is no Van der Waals like black hole and small black hole phase transition. After that, we focus on the correspondence between van der Waals transition and dynamical stability of black hole. The thermodynamic phase transition can be reflected in the quasi-positive scale frequency and the attenuation time of oscillations around the black hole. We investigate the scalar perturbation of the large black hole phase and the small black hole phase in the process of the black hole van der Waals phase transition. We find that it is not only in isobaric process but also in isothermal process. Changes with the radius of the black hole's event horizon. The behavior of quasi-positive frequency in large black hole phase and small black hole phase is very different. This kind of similar positive scale frequency difference in large black hole and small black hole can distinguish the thermodynamic phase of black hole. We further analyze the influence of black hole resemblance. The factor of positive scale frequency. A new example is provided for the reflection of the thermodynamic phase transition of black hole in the dynamic stability of black hole. Finally, we discuss the scalar of three-dimensional space-time band. Black hole solution of Mao. By setting appropriate scalar potential function. 桅). We have obtained a new solution of turbid black hole with hair, and the thermodynamic quantity of this new solution satisfies the first law of thermodynamics of black hole. Next, an electromagnetic disturbance is added to the background of black hole space-time. We calculate the lowest order frequency of electromagnetic disturbances of a rotating black hole with scalar hairs. It is found that the variation of the imaginary part of the quasi-positive frequency corresponds to the thermodynamic stability. This conclusion is also applicable to the solution of the static haired black hole in three-dimensional space-time.
【学位授予单位】：上海交通大学
【学位级别】：博士
【学位授予年份】：2015
【分类号】：P145.8

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