Non-Markovian dynamics of black hole phase transition

TL;DR

This paper investigates the non-Markovian stochastic dynamics of black hole phase transitions using generalized Langevin equations, analyzing how different memory effects influence transition times and revealing resonance phenomena.

Contribution

It introduces a detailed analytical framework for non-Markovian black hole phase transition dynamics with various friction kernels, highlighting the impact of memory effects.

Findings

Non-Markovian effects can slow or speed up phase transitions depending on friction strength.

Kinetic resonance occurs when oscillation frequencies of the bath and black hole states match.

Different friction kernels significantly influence the transition dynamics and timescales.

Abstract

We provide a comprehensive study on the non-Markovian dynamics of the black hole phase transitions based on the underlying free energy landscape. 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 RNAdS 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.