Hawking-Page phase transition in BTZ black hole revisited

TL;DR

This paper revisits the Hawking-Page phase transition in BTZ black holes, analyzing off-shell free energies and tunneling effects, revealing a continuous transition facilitated by non-equilibrium states.

Contribution

It introduces a consistent method to construct off-shell free energies for BTZ black holes and solitons, accounting for conical spaces and tunneling effects.

Findings

Off-shell free energies are constructed considering conical spaces.

A continuous phase transition is possible via non-equilibrium solitons.

The analysis clarifies the thermodynamic behavior of BTZ black holes and solitons.

Abstract

We consider the Hawking-Page phase transition between the BTZ black hole of $M \ge 0$ and the thermal soliton of $M=-1$. In this system, there exists a mass gap so that there does not seem to exist a continuous thermodynamic phase transition. We consistently construct the off-shell free energies of the black hole and the soliton by properly taking into account the conical space. And then, the continuous off-shell free energy to describe tunneling effect can be realized through non-equilibrium solitons.