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arXiv 1403.4356gr-qc
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黑洞中的相变

Phase transition in black holes

Dibakar Roychowdhury

摘要:

本论文致力于研究定义在反德西特(AdS)空间中的黑洞的相变现象的各个方面。基于热力学的基本原理,并考虑一个巨正则框架,我们研究的各个方面的相变现象发生在AdS黑洞。我们分析检查,这个相变之间的较小的和较大的质量黑洞遵守在临界点定义的Ehrfest关系,从而确认二阶相变。这包括爱因斯坦引力中的旋转和带电黑洞。除了研究这些问题外,我们还在正则框架下研究了带电AdS黑洞的临界行为。这些黑洞的标度律与静态标度假设是相容的。最后,基于AdS/CFT对偶的一般框架,我们研究了定义在渐近AdS空间中的带电多毛黑洞的相变现象。在解析计算的基础上,利用AdS/CFT字典,我们明确地计算了在相变临界点附近对偶CFT的序参量,并发现与凝聚相关联的临界指数为$\frac{1}{2}$,这是平均场论的普遍结果.此外,我们还发现在外加磁场的作用下,双CFT在低温下表现出完全抗磁性,这可能是所谓的迈斯纳效应的一种联想。

英文摘要:

The present thesis is devoted towards the study of various aspects of the phase transition phenomena occurring in black holes defined in an Anti-de-Sitter (AdS) space. Based on the fundamental principles of thermodynamics and considering a grand canonical framework we examine various aspects of the phase transition phenomena occurring in AdS black holes. We analytically check that this phase transition between the smaller and larger mass black holes obey Ehrenfest relations defined at the critical point and hence confirm a second order phase transition. This include both the rotating and charged black holes in Einstein gravity. Apart from studying these issues, based on a canonical framework, we also investigate the critical behavior in charged AdS black holes. The scaling laws for these black holes are found to be compatible with the static scaling hypothesis. Finally, based on the usual framework of AdS/CFT duality, we investigate the phase transition phenomena occurring in charged hairy black holes defined in an asymptotically AdS space. Based on analytic calculations, and using the AdS/CFT dictionary, we explicitly compute the order-parameter for the dual CFT close to the critical point of the phase transition and found that the critical exponent associated with the condensation is $\frac{1}{2}$, which is the universal result of the mean field theory. Moreover, we also find that in the presence of an external magnetic field, the dual CFT exhibit a perfect diamagnetism at low temperatures, which may be regarded as the reminiscent of the so called Meissner effect.

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