Phase transitions in Bergshoeff-Hohm-Townsend Massive Gravity

TL;DR

This paper explores the phase transitions of various black hole solutions in Bergshoeff-Hohm-Townsend massive gravity, revealing ensemble-dependent symmetries and providing detailed phase diagrams for different spacetime configurations.

Contribution

It provides the first comprehensive analysis of Hawking-Page phase diagrams for multiple black hole solutions in BHT massive gravity, highlighting ensemble effects and symmetry properties.

Findings

Phase diagrams vary significantly across ensembles.

Symmetry with respect to angular momentum is observed except in quadratic ensemble.

Grand canonical ensemble is recommended for warped AdS3 black holes.

Abstract

We present the Hawking-Page phase diagrams in the Bergshoeff-Hohm-Townsend (BHT) massive gravity theory for different solutions, such as the phase transitions between vacuum $\text{AdS}_3$ and BTZ black hole, warped $\text{AdS}_3$ and warped BTZ black hole in grand canonical and in non-local/quadratic ensembles, Lifshitz black hole and the new hairy black hole solutions. We observe that except for the black holes in quadratic ensemble, for other cases in the non-chiral theory of BHT the phase diagrams are symmetric with respect to the direction of angular momentum, as we expected. We conclude that for presenting the phase diagrams of warped $\text{AdS}_3$ black holes, only the grand canonical ensemble should be used.