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 and BTZ black hole, warped 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 black holes, only the grand canonical ensemble should be used.