Phase transitions in Bergshoeff-Hohm-Townsend Massive Gravity

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.