Thermal radiation and nonthermal radiation of the slowly changing dynamic Kerr--Newman black hole

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.