Effects of a global monopole on thermodynamic phase transition of the charged AdS black hole

TL;DR

This paper investigates how a global monopole influences the thermodynamic phase transition dynamics of charged AdS black holes, revealing that monopoles slow down state evolution and increase the mean first passage time.

Contribution

It introduces the Gibbs free energy landscape and Fokker-Planck equation approach to study monopole effects on black hole phase transition kinetics, a novel application in this context.

Findings

Global monopoles slow down black hole state transitions.

The mean first passage time increases with the monopole parameter.

Monopoles affect the thermodynamic stability and transition rates.

Abstract

In this paper, we study the dynamical properties of thermodynamic phase transition (PT) for the charged AdS black hole (BH) with a global monopole via the Gibbs free energy landscape and reveal the effects of a global monopole on the kinetics of the AdS BH thermodynamic PT. First, we briefly review the thermodynamics of the charged AdS BH with a global monopole. Then, we introduce the Gibbs free energy landscape to study the thermodynamic stability of the BH state. Because of thermal fluctuations, the small black hole (SBH) state can transit to the large black hole (LBH) state, and vice versa. We use the Fokker-Planck equation with the reflecting boundary condition to study the probability evolution of the BH state with and without a global monopole separately. We find that for both the SBH and LBH states, the global monopole could slow down the evolution of the BH state. In addition, we obtain the relationship between the first passage time and the monopole parameter $\eta$. The result shows that as the monopole parameter $\eta$ increases, the mean first passage time will be longer for both the SBH and LBH states.