Reentrant Hawking-Page phase transition of the general BTZ black holes

Recent researches about three dimensional gravity show that there is a family of the "exotic" black holes which the roles of the mass and angular momentum are reversed, named as the general exotic BTZ black holes. In this paper, we investigate the Hawking-Page (HP) phase transition of the general exotic BTZ black holes, which involve a mixture of actions including the Einstein-Hilbert action alpha(IEH) I EH ) and the Chern-Simons action gamma ( I GCS ). The HP transitions of the exotic general BTZ black holes have a complicated phase structure. We find that for the "more normal" BTZ black holes (alpha >= gamma , i.e. alpha >= 1/2), there always exists a standard HP transition which is similar to the cases in Einstein gravity. For the "more exotic" BTZ black holes (alpha < gamma , i.e. alpha < 1/2), an emergent branch of the more-stable large black holes (LBHs) results in a zeroth-order HP like transition. As a result, the system always undergoes a reentrant HP transition from the AdS vacuum to BHs, and then back to the AdS vacuum phase, as the temperature increases. In particular, for the constant alpha(c) < alpha < 1/2, the reentrant HP transition consists of two zeroth-order HP like transitions. For the pure "exotic" BTZ black hole with alpha = 0, there is no HP transition.