Abstract Using entropy density of Dirac field near the event horizon of a rectilinear non-uniformly accelerating Kinnersley black hole, the law for the thermal radiation of black hole is studied and the instantaneous radiation energy density is obtained. It is found that the instantaneous radiation energy density of a black hole is always proportional to the quartic of the temperature on event horizon in the same direction. That is to say, the thermal radiation of a black hole always satisfies the generalized Stefan--Boltzmann law. In addition, the derived generalized Stefan--Boltzmann coefficient is no longer a constant, but a dynamic coefficient related to the space--time metric near the event horizon and the changing rate of the event horizon in black holes.
Received: 29 April 2008
Revised: 18 August 2008
Accepted manuscript online:
PACS:
04.70.Dy
(Quantum aspects of black holes, evaporation, thermodynamics)
Fund: Project supported by
the National Natural Science Foundation of China (Grant No 10773002)
and the Technology Planning Project of
Education Bureau of Shandong Province, China (Grant No J07WJ49).
Cite this article:
Jiang Ji-Jian(蒋继建), Meng Qing-Miao(孟庆苗), and Wang Shuai(王帅) The generalized Stefan--Boltzmann law of a rectilinear non-uniformly accelerating Kinnersley black hole 2009 Chin. Phys. B 18 457
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