The kinetics and its turnover of Hawking-Page phase transition under the black hole evaporation

The thermodynamics and the kinetics of Hawking-Page phase transition were studied previously based on the free energy landscape. The AdS black hole can evaporate if imposing the absorbing boundary conditions at infinity. We suggest that the kinetics of Hawking-Page phase transition should be governed by the reaction-diffusion equation, where the Hawking evaporation plays the role of the reaction on the background of the free energy landscape. By calculating the mean first passage time from the large black hole phase to the thermal gas phase, we show that the phase transition can occur more easily under the Hawking radiation. In particular, a kinetic turnover is observed when increasing the ensemble temperature or the frictions. This kinetic turnover can be viewed as the dynamical phase transition to identify the time scale where Hawking evaporation process is comparable to Hawking-Page phase transition.