Thermodynamics of rotating black holes with scalar hair in three dimensions

TL;DR

This paper derives a new rotating black hole solution with scalar hair in three-dimensional Einstein gravity, analyzes its thermodynamics, phase transitions, and compares it with the BTZ black hole, revealing thermodynamic preferences.

Contribution

It introduces a novel scalar potential and solution for rotating hairy black holes in three dimensions, and studies their thermodynamic properties and phase transitions.

Findings

First law of thermodynamics is preserved for the new solution.

Hawking-Page phase transition occurs between hairy black holes and thermal radiation.

BTZ black holes are thermodynamically favored over hairy black holes.

Abstract

Introducing a new form of scalar potential $V(\phi)$, we derive a proper form of the rotating black hole solution in three-dimensional Einstein gravity with nonminimally coupled scalar field and find that the first law of thermodynamics of this new rotating hairy black hole can be protected, where the scalar field parameter $B$ is constrained to relate to the black hole size. We also disclose the Hawking-Page phase transition between this rotating hairy black holes and the pure thermal radiation. Moreover, we study phase transitions between this rotating hairy black hole and rotating BTZ black hole. Considering the matchings for the temperature and angular momentum, we find that the rotating BTZ black hole always has smaller free energy which is a thermodynamically more preferred phase. Additionally, we evaluate the thermodynamics of the rotating black hole with minimally coupled scalar hair in three dimensions, which exhibits that the thermodynamical behaviors of this rotating hairy black hole are very similar to those of the rotating black hole with nonminimally coupled scalar hair.