Thermodynamics and Phase Transition of a Gauss-Bonnet Black Hole in a Cavity

TL;DR

This paper studies the thermodynamics and phase transitions of Gauss-Bonnet black holes within a finite cavity, revealing phase coexistence, transitions, and similarities to black holes in anti-de Sitter space.

Contribution

It provides a detailed analysis of phase structures and transitions of Gauss-Bonnet black holes in a cavity, extending understanding of black hole thermodynamics in finite systems.

Findings

Existence of single and multiple phases depending on parameters

Observation of van der Waals-like phase transition

Thermodynamic similarities with Gauss-Bonnet-Maxwell black holes in AdS space

Abstract

Considering a canonical ensemble, in which the temperature and the charge on a wall of the cavity are fixed, we investigate the thermodynamics of a D-dimensional Gauss-Bonnet black hole in a finite spherical cavity. Moreover, it shows that the first law of thermodynamics is still satisfied. We then discuss the phase structure and transition in both five and six dimensions. Specifically, we show that there always exist two regions in the parameter space. In one region, the system possesses one single phase. However in the other region, there could coexist three phases and a van der Waals-like phase transition occurs. Finally, we find that there is a fairly close resemblance in thermodynamic properties and phase structure of a Gauss-Bonnet-Maxwell black hole, either in a cavity or in anti-de Sitter space.