Extended Phase Space Thermodynamics for Black Holes in a Cavity

TL;DR

This paper explores the thermodynamics of black holes within a cavity, revealing phase transitions similar to those in anti-de Sitter spaces and van der Waals fluids, thus offering new insights into black hole thermodynamics.

Contribution

It extends black hole thermodynamics to include cavity volume, establishing parallels with AdS black holes and fluid systems, and uncovers phase transition behaviors in this new framework.

Findings

First-order phase transition for Schwarzschild black holes in a cavity.

Reissner-Nordstrom black holes exhibit van der Waals-like phase structure.

Thermodynamic behavior in a cavity mirrors that of AdS black holes with a cosmological constant.

Abstract

In this paper, we extend the phase space of black holes enclosed by a spherical cavity of radius $r_{B}$ to include $V\equiv4\pi r_{B}^{3}/3$ 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. Our results may provide a new perspective for the extended thermodynamics of AdS black holes by analogy with black holes in a cavity.