Using the related formula of dynamic black hole, we have calculated the instantaneous radiation energy density of the slowly changing dynamic Kerr-Newman black hole. It is found that the instantaneous radiation energy density of a black hole is always proportional to the quartic of the temperature of the event horizon in the same direction. By using the Hamilton-Jacobin equation of scalar particles in the curved spacetime, the spontaneous radiation of the slowly changing dynamic Kerr-Newman black hole is studied. The energy condition for the occurrence of the spontaneous radiation is obtained.
Using entropy density near event horizon of the non-stationary Dilaton-Maxwell black hole, the instantaneous emission flux is calculated, and we come to a conclusion that the instantaneous emission flux of blank hole in any direction at any time is always proportionate to the quartic power of temperature of the event horizon of black hole in that direction. It is found that the coefficient of generalized Stefan-Boltzmann is no longer a constant, but a dynamic proportional coefficient related to the rate of change of event horizon, the structure of space-time near event horizon and the radiation absorption coefficient of black hole. It shows that an inner relation between the gravitational field around black hole and its thermal radiation must exist.
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