Thermodynamics and kinetics of Hawking-Page phase transition

Abstract

We study the thermodynamics and the kinetics of the Hawking-Page phase transition in Einstein gravity and in massive gravity based on the underlying free energy landscape. For Einstein gravity, Schwarzschild--anti-de Sitter (AdS) black holes as well as thermal AdS space can be considered as macroscopic emergent states or phases. The stability and phase transition of these states can be determined by free energy landscape topography quantified by the barrier height between the state basins. Due to the thermal fluctuations, a black hole or AdS space has the chance to escape from one phase to another phase. The first passage process describes a system that undergoes such a kinetic process for the first time, and the mean first passage time can typically be used to quantify the kinetic speed. The probabilistic evolution of such a stochastic process can be described by the corresponding Fokker-Planck equation. We derive analytical integral expressions for the mean first passage time and its fluctuations. The results show that the mean first passage time and its fluctuations are closely related to free energy landscape topography through barrier heights and the temperature. The conclusions for the Hawking-Page phase transition in massive gravity are qualitatively similar to those in Einstein gravity. This study provides a systematic way of studying black hole thermodynamics and kinetics of the black holes from free energy landscape topography.