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

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.

Non-Markovian dynamics of black hole phase transition

“…For the intermediate friction ζ = 3.5, the competition of the two behaviors leads to the non-monotonic behavior of the transition rate with respect to the decay coefficient γ as shown in Figure 8. Note that the speed up behavior of the transition process in the large friction regime has been observed previously [33]. The reason behind is that the non-Markovian effect introduces more time scales and therefore equivalently more degrees of freedom.…”

“…The generalized Langevin equation is an integro-differential equation where the integral term reflects the memory effect or the non-Markovian effect of the effective thermal bath from the underlying degrees of freedom of the black hole. It should be noted that the framework of the non-Markovian model of black hole phase transition has been briefly introduced in [33], where the transition rate of the non-Markovian dynamics of black hole phase transition was derived and used to study the kinetics of the Hawking-Page phase transition. It was shown that the non-Markovian effect or the memory effect can promote the dynamical process of Hawking-Page phase transition.…”

“…It is shown that the analytical expressions of the MFPT in the intermediate friction regime also includes the one applied in the strong friction regime. Note that the transition rate derived in [33] is only valid in the intermediate-strong friction regime. By employing the analytical expressions of the MFPTs in the intermediate and weak friction regimes, the bridging formula of the MFPT for the black hole phase transition is explicitly given [39,40].…”