Hawking-Page transition with reentrance and triple point in Gauss-Bonnet gravity
Yuan-zhang Cui, Wei Xu, Bin Zhu
Abstract
In this paper, a new family of Hawking-Page transitions, i.e., Hawking-Page transitions with reentrance and a triple point, is introduced for the first time by investigating the Hawking-Page transition of hyperbolic AdS black holes in the extended thermodynamics in Gauss-Bonnet gravity. The reentrant Hawking-Page transition is composed of two Hawking-Page transitions with a high and a low Hawking-Page temperature, and the triple point corresponds to small black hole, massless black hole, and large black hole phases all coexisting. We discuss the temperatures of two branches of Hawking-Page transitions, which both depend on the pressure (i.e., the cosmological constant) and the Gauss-Bonnet constant. The pressure and the Gauss-Bonnet constant both increase the high Hawking-Page temperature and diminish the low Hawking-Page temperature. We also show the coexistence lines in the $P\ensuremath{-}T$ phase diagrams. The triple point and critical point in the phase diagrams of the Gauss-Bonnet AdS black hole systems are given, together with some interesting universal relations that only depend on the dimensions of spacetime. The reentrant Hawking-Page transition and triple point may correspond to the phase transition and triple point in the QCD phase diagram, following the spirit of the $\mathrm{AdS}/\mathrm{CFT}$ correspondence. These results may improve the comprehension of the black hole thermodynamics in the quantum gravity framework and shed some light on the $\mathrm{AdS}/\mathrm{CFT}$ correspondence beyond the classical gravity limit.