Thermodynamics and phase transition of BTZ black hole in a cavity

TL;DR

This paper investigates the thermodynamics and phase transitions of BTZ black holes within a finite cavity, revealing stability conditions and unique phase behaviors compared to black holes without a cavity.

Contribution

It derives thermodynamic properties and phase transition characteristics of BTZ black holes in a cavity, highlighting differences from traditional black hole thermodynamics.

Findings

Heat capacities are always non-negative.

Rotating and charged black holes are locally thermodynamically stable.

Distinct phase transition behaviors occur due to the cavity presence.

Abstract

In this paper, we study the thermodynamics and phase transition of a BTZ black hole in a finite space region, namely a cavity. By imposing a temperature-fixed boundary condition on the wall of the cavity and evaluating the Euclidean action, we derive the thermodynamic quantities and then construct the first law of thermodynamics for a static and neutral BTZ black hole, a rotating BTZ black hole and a charged BTZ black hole, respectively. We prove that heat capacities of these three types of black holes are always non-negative. Considering a grand canonical ensemble, we find that the non-extreme rotating black hole and the charged black hole are locally thermodynamically stable by calculating the Hessian matrix of their internal energy. At the phase transition level, it shows that for the static and neutral BTZ black hole, the phase transition only exists between thermal AdS3 spacetime and the black hole. The temperature where the phase transition occurs is only determined by the cavity radius. For rotating and charged cases, there may exist an extra second-order phase transition between the black hole and the black hole-cavity merger state. The phase structure of a BTZ black hole in a cavity shows strong dissimilarities from that without the cavity.