The critical behaviors of the black holes with the generalized uncertainty principle

Abstract

After considering the effect of the generalized uncertainty principle (GUP), we investigate the thermodynamic critical behaviors of the Schwarzschild-AdS (SAdS) black hole and the Reissner-Nordström-AdS (RN-AdS) black hole in four-dimensional spacetime. It is shown that for the SAdS black hole the Hawking-Page phase transition no longer always occurs under a certain condition which is replaced by a zero-order phase transition from the thermal AdS space to the large stable black hole. For the RN-AdS black hole, besides the usual small/large black-hole phase transition, an interesting reentrant phase transition also appears. This critical behavior is very similar to that of the Kerr-AdS black hole in higher-dimensional spacetime .