Mean first passage time and the Kramers escape rate of phase transitions for the Bardeen-AdS-class black hole

TL;DR

This paper analyzes phase transitions in Bardeen-AdS black holes using stochastic dynamics, revealing different transition pathways involving stable, metastable, and vacuum states.

Contribution

It introduces a comprehensive landscape of black hole phase transitions using Mean First-Passage Time and Kramers escape rate, highlighting distinctions between solution types.

Findings

Type I black holes transition through regular black hole states.

Type II black holes transition directly between vacuum and small black holes.

Different transition pathways depend on black hole solution category.

Abstract

In this study, by utilizing the constructed generalized free energy alongside the Mean First-Passage Time and the Kramers escape rate from stochastic dynamics, we have obtained a comprehensive landscape of the phase transitions for the Bardeen-AdS-class black hole. This black hole model admits two distinct categories of solutions. Type I black holes feature a regular black hole solution, and Type II black holes possess a vacuum state solution. In the phase transition between the small black hole and the large black hole for Type I, the process may pass through a stable, metastable, or unstable regular black hole as an intermediate state. In contrast, for Type II black holes, the phase transition occurs exclusively between the vacuum state and the small black hole, and the transition process does not involve any regular black hole intermediate states.