Thermodynamics of rotating black holes with scalar hair in three dimensions

Abstract

Introducing a new form of scalar potential $V(\varphi )$, 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.

15 pages, 4 figures, minor changes, To be published in Phys. Rev. D

References in corpus (8)

• Electromagnetic Properties of Kerr-Anti-de Sitter Black Holes
• Electrically charged black hole with scalar hair
• Quasi-normal Modes of Electromagnetic Perturbations of Four-Dimensional Topological Black Holes with Scalar Hair
• Thermodynamical properties of hairy black holes in n spacetimes dimensions
• Phase transition for black holes with scalar hair and topological black holes
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• Joule-Thomson expansion of Lower-dimensional black hole
• Exact black hole formation in three dimensions
• Analytic three-dimensional primary hair charged black holes and thermodynamics
• Quasinormal modes of charged BTZ black holes
• Information evolution in the interior of an axially symmetric BTZ black hole
• A new rotating axionic AdS${}_4$ black hole dressed with a scalar field