Dynamics and kinetics of phase transition for regular AdS black holes in general relativity coupled to nonlinear electrodynamics

We study the stochastic dynamics and kinetics of the phase transition of the regular black holes in Anti-de Sitter spacetime by employing the free energy landscape. Our investigation focuses on two important classes of regular black hole solutions, namely the Hayward and Bardeen, which can be obtained from coupling of non-linear electrodynamics. The dynamics of the phase transition is described by the Fokker-Planck equation, using which, we investigate the probabilistic evolution of regular AdS black holes. We solve this equation numerically by imposing both reflecting and absorbing boundary conditions and appropriate initial conditions. In this context, the on-shell Gibbs free energy is treated as a function of the event horizon radius, where the difference of the event horizon radii in different phases serves as the order parameter for the phase transition. The study allows us to probe the dynamic process of transitioning between coexisting small and large black hole phases due to thermal fluctuations, as quantified by the calculation of the first passage time. Furthermore, we explore the influence of temperature on this dynamic process. This research contributes to a deeper understanding of the microstructures of regular AdS black holes.