Thermodynamics and phase transitions of black holes in contact with a gravitating heat bath

TL;DR

This paper investigates the thermodynamics and phase transitions of self-gravitating radiation shells, revealing four distinct phases including black holes, flat space, and naked singularities, with a focus on black hole phase transitions and stability.

Contribution

It introduces a consistent thermodynamic model for gravitating systems with boundaries, incorporating boundary entropy terms, and analyzes phase transitions among multiple gravitational solutions.

Findings

Identification of four thermodynamic phases including two black hole types

Analysis of black hole phase transitions and stability criteria

Characterization of the non-concave entropy and temperature behavior

Abstract

We study the thermodynamics of a shell of self-gravitating radiation, bounded by two spherical surfaces. This system provides a consistent model for a gravitating thermal reservoir for different solutions to vacuum Einstein equations in the shell's interior. The latter include black holes and flat space, hence, this model allows for the study of black hole phase transitions. Following the analysis of arXiv:1103.3898 , we show that the inclusion of appropriate entropy terms to the spacetime boundaries (including the Bekenstein-Hawking entropy for black hole horizons) leads to a consistent thermodynamic description. The system is characterized by four phases, two black hole phases distinguished by the size of the horizon, a flat space phase and one phase that describes naked singularities. We undertake a detailed analysis of black-hole phase transitions, the non-concave entropy function, the properties of temperature at infinity, and system's heat capacity.