Astronomy and Astrophysics – Astrophysics – General Relativity and Quantum Cosmology
Scientific paper
2004-10-08
Class.Quant.Grav. 22 (2005) 2671-2678
Astronomy and Astrophysics
Astrophysics
General Relativity and Quantum Cosmology
Accepted for publication in Classical and Quantum Gravity
Scientific paper
10.1088/0264-9381/22/13/010
This paper demonstrates a dynamical evolution model of the black hole (BH) horizon. The result indicates that a kinetic area-cells model of the BH's horizon can model the evolution of 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 the energy like a microscopic black hole, and has the gravitational interaction with the other area-cells. We consider both a non-interaction ideal system, and a system with small nearest-neighbor 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.
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