Non-Markovian dynamics of black hole phase transition
Ran Li, Jin Wang
Abstract
We provide a comprehensive study on the non-Markovian dynamics of the black hole phase transitions based on the underlying free energy landscape. In general, there are two typical timescales to characterize non-Markovian dynamics: (i) the timescale of the system represented by the intrinsic oscillating time of the black hole state at the potential well on the free energy landscape; (ii) the correlation time of the effective thermal bath. By assuming that the transition processes between different black hole states are stochastic, the non-Markovian dynamics of the black hole phase transition is governed by the generalized Langevin equation with the time-dependent friction that represents the memory effect from the effective thermal bath when the timescale of the system is comparable or shorter than the timescale of the effective thermal bath. We consider the first passage problem associated with the black hole phase transitions and derive the analytical expressions of the mean first passage time in the weak, intermediate, and large friction regimes. As the concrete examples, we study the effects of three types of time dependent friction kernel (delta function friction, exponentially decayed friction, and oscillatory friction) on the dynamics of Hawking-Page phase transition and the small/large Reissner-Nordstr\"om anti--de Sitter black hole phase transition. We found that there is a kinetic turnover point for each type of friction kernel when the friction strength varies. For the exponentially decayed friction kernel, it is shown that the non-Markovian effect slows down the phase transition dynamics in the weak friction regime and speeds up the transition process in the strong friction regime. For the oscillating decayed friction kernel, we found kinetic resonances when the oscillating frequency of the effective thermal bath is equal to the oscillating frequency of the black hole state in the initial potential well on the free energy landscape.