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

We study the dynamical properties of the thermodynamic phase transition(PT) of a charged AdS black hole(BH) with a global monopole via the Gibbs free energy landscape and reveal the effects of the global monopole on the kinetics of thermodynamic PTs. First, we briefly review the thermodynamics of a charged AdS BH with a global monopole. Then, we introduce the Gibbs free energy landscape to investigate the thermodynamic stability of the BH states. Because of thermal fluctuations, the small black hole(SBH) state can transit to a large black hole(LBH) state, and vice versa. Further, 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. It is found 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 η. The result shows that as the monopole parameter η increases, the mean first passage time becomes longer for both the SBH and LBH states.