Phase transitions and thermodynamic geometry of a Kerr-Newman black hole in a cavity

TL;DR

This paper explores the thermodynamic phase transitions and microscopic interactions of Kerr-Newman black holes in a cavity, revealing similarities in phase behavior but differences in microstructure compared to related black holes.

Contribution

It introduces a detailed thermodynamic analysis of Kerr-Newman black holes in a cavity, including phase transitions and thermodynamic geometry, highlighting microstructure sensitivities.

Findings

Black holes exhibit van der Waals-like phase transitions in a cavity.

Thermodynamic geometry reveals microstructure differences despite similar phase structures.

Microstructure of black holes is sensitive to their thermodynamic states.

Abstract

Being placed in a cavity is an effective way of reaching thermodynamic equilibrium for black holes. We investigate a Kerr-Newman black hole in a cavity as well as compare it with two reduced cases, i.e., a RN black hole in a cavity and a Kerr black hole in a cavity. We derive the quasi-local energy from the Hamiltonian, and construct the first law of thermodynamics accordingly. In a canonical ensemble, these black holes could undergo a van der Waals-like phase transition, which is very similar to that in AdS space. We further investigate the black holes' thermodynamic geometry, which is a powerful tool to diagnose microscopic interactions of a thermodynamic system. Our results show that in a cavity, although phase structures of these black holes are similar, their thermodynamic geometry show strong dissimilarities, implying that the microstructure of a black hole is sensitive to its states.