Kinetics of Hawking-Page phase transition with the non-Markovian effects

TL;DR

This paper investigates how non-Markovian effects, modeled via generalized Langevin equations with specific friction kernels, influence the kinetics of Hawking-Page phase transitions between black holes and thermal AdS space.

Contribution

It introduces a non-Markovian framework to study the kinetics of Hawking-Page phase transitions, highlighting the impact of memory effects on transition rates.

Findings

Exponential decay friction kernel accelerates the phase transition.

Oscillatory friction kernel's frequency increases transition speed.

Non-Markovian effects can significantly alter transition kinetics.

Abstract

Based on the free energy landscape description of Hawking-Page phase transition, the transition process from the Schwarzschild-anti-de Sitter black hole to the thermal anti-de Sitter space are considered to be stochastic under the thermal fluctuations. If the correlation time of the effective thermal bath is comparable or even longer than the oscillating time of the spacetime state in the potential well on the free energy landscape, the non-Markovian model of the black hole phase transition is required to study the kinetics of the transition processes. The non-Markovian or memory effect is represented by the time dependent friction kernel and the kinetics is then governed by the generalized Langevin equation complemented by the free energy potential. As the concrete examples, we study the effects of the exponentially decay friction kernel and the oscillatory friction kernel on the kinetics of Hawking-Page phase transition. For the exponentially decayed friction, the non-Markovian effects promote the transition process, and for the oscillatory friction, increasing the oscillating frequency also speeds up the transition process.