Thermodynamic Geometry of Black Holes Enclosed by a Cavity in Extended Phase Space

TL;DR

This paper explores the thermodynamic geometry of charged black holes in a cavity within an extended phase space, revealing differences from AdS black holes and identifying a reentrant microstructure interaction transition.

Contribution

It introduces the thermodynamic geometry analysis for RN black holes in a cavity and compares it with AdS black holes, highlighting novel reentrant transition behavior.

Findings

Reentrant transition of microstructure interactions in RN black holes in a cavity.

Significant differences in thermodynamic geometries between cavity and AdS black holes.

Identification of microstructure interaction changes with temperature.

Abstract

Recently, the phase space of black holes in a spherical cavity of radius $r_{B}$ has been extended by introducing a thermodynamic volume $V\equiv4\pi r_{B}^{3}/3$. In the extended phase space, we consider the thermodynamic geometry, which provides a powerful tool to understand the microscopic structure of black holes, of Reissner-Nordstr\"{o}m (RN) black holes in a cavity, as well as that of Reissner-Nordstr\"{o}m-AdS black holes. Although the phase structures of the cavity and AdS cases show striking resemblance, we find that there exist significant differences between the thermodynamic geometries of these two cases. In particular, a reentrant transition of the type of the microstructure interactions, i.e., repulsive $\rightarrow$ attractive $\rightarrow$ repulsive with increasing temperature in an isobaric process, is observed for RN black holes in a cavity.