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arXiv 2012.13921gr-qc
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腔中黑洞的Hawking-Page相变

Hawking--Page phase transitions of the black holes in a cavity

Wen-Bo Zhao, Guo-Rong Liu, Nan Li

备注：
20 pages, 5 figures
发表信息：
Eur. Phys. J. Plus 136, 981 (2021)
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摘要：

在扩展相空间中研究了Schwarzschild黑洞和带电黑洞的Hawking-Page相变，其中黑洞被封闭在渐近平坦空间中半径为$r_B$的球形空腔中.引入黑洞的有效热力学体积$V=4πr_B^3/3$，定义有效压力$p$作为$V$的共轭变量.在固定电势$Φ$的巨正则系综中系统地研究了相变温度$T_{\rm HP}$和吉布斯自由能$G$，发现$T_{\rm HP}$随$p$增大而随$Φ$减小.如果发生相变，$Φ$必须有一个上限，使得空腔半径总是大于黑洞视界半径。进一步将这些相变行为与反deSitter空间中的相变行为进行了比较，并深入讨论了它们之间的显著相似性和显著差异。我们的工作揭示了黑洞的热力学性质与其特定边界条件在不同扩展相空间中的关系。

英文摘要：

The Hawking--Page phase transitions of the Schwarzschild and charged black holes are investigated in an extended phase space, in which the black holes are enclosed in a spherical cavity of radius $r_B$ in asymptotically flat space. An effective thermodynamic volume $V=4πr_B^3/3$ is introduced for the black hole, and an effective pressure $p$ is defined as the conjugate variable of $V$. The phase transition temperature $T_{\rm HP}$ and the Gibbs free energy $G$ are systematically studied in a grand canonical ensemble with fixed electric potential $Φ$, and $T_{\rm HP}$ is found to increase with $p$ and decrease with $Φ$. If the phase transition occurs, $Φ$ must have an upper bound, such that the cavity radius is always larger than the black hole horizon radius. These phase transition behaviors are further compared to those in the anti-de Sitter space, and the remarkable similarities and notable differences are also discussed in depth. Our work reveals the relationship of the thermodynamic properties of black holes and their specific boundary conditions in different extended phase spaces.

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