A dynamical evolution model on the black-hole horizon

Abstract

This paper demonstrates a dynamical evolution model of the black-hole (BH) horizon. The result indicates that a kinetic area-cell model of the BH horizon can model the evolution of the BH due to the Hawking radiation, and this area-cell system can be considered as an interacting geometrical particle system. Thus, the evolution turns into a problem of statistical physics. In the present work, this problem is treated in the framework of non-equilibrium statistics. It is proposed that each area cell possesses energy like a microscopic black hole and has gravitational interaction with the other area cells. We consider both a non-interaction ideal system and a system with small nearest-neighbour interactions, and obtain an analytic expression of the expected value of the horizon area of a dynamical BH. We find that, after a long enough evolution, a dynamical BH with the Hawking radiation can be in equilibrium with a finite-temperature radiation field. However, we also find that the system has a critical point, and when the temperature of the radiation field surrounding the BH approaches the critical temperature of the BH, a critical slowing-down phenomenon occurs.