In this paper, we extend the phase space of black holes enclosed by a spherical cavity of radius rB to include $$ V=4\pi {r}_B^3/3 $$ as a thermodynamic volume. The thermodynamic behavior of Schwarzschild and Reissner-Nordstrom (RN) black holes is then investigated in the extended phase space. In a canonical ensemble at constant pressure, we find that the aforementioned thermodynamic behavior is remarkably similar to that of the anti-de Sitter (AdS) counterparts with the cosmological constant being interpreted as a pressure. Specifically, a first-order Hawking-Page-like phase transition occurs for a Schwarzschild black hole in a cavity. The phase structure of a RN black hole in a cavity shows a strong resemblance to that of the van der Waals fluid. We also display that the Smarr relation has the same expression in both AdS and cavity cases. Our results may provide a new perspective for the extended thermodynamics of AdS black holes by analogy with black holes in a cavity.

中文翻译：

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空腔中黑洞的扩展相空间热力学

在本文中，我们扩展了由半径为 rB 的球腔包围的黑洞的相空间，以包含 $$ V=4\pi {r}_B^3/3 $$ 作为热力学体积。然后在扩展相空间中研究 Schwarzschild 和 Reissner-Nordstrom (RN) 黑洞的热力学行为。在恒定压力下的正则系综中，我们发现上述热力学行为与反德西特 (AdS) 对应物的热力学行为非常相似，宇宙学常数被解释为压力。具体来说，空腔中的施瓦兹希尔德黑洞会发生一阶霍金佩奇相变。空腔中 RN 黑洞的相结构与范德华流体的相结构非常相似。我们还表明 Smarr 关系在 AdS 和空腔情况下具有相同的表达式。