Charged Hawking radiation and the entropy variation in a Reissner–Nordström black hole

Abstract

Under charged Hawking radiation, we calculate the entropy of the scalar field in the interior volume of a Reissner–Nordström (RN) black hole and investigate the proportional relation between this entropy and the Bekenstein–Hawking entropy. Comparing with uncharged Hawking radiation, we find that whether the particles radiated from the black hole are charged cannot affect the proportional relation between the two types of entropy. Furthermore, the proportionality coefficient of the two types of entropy has been analyzed and discussed. The result shows that the variation of scalar field entropy inside the black hole is approximately proportional to the variation of Bekenstein–Hawking entropy in an infinitesimal evaporation process. Moreover, the proportional relation can degenerate to the Schwarzschild case when the charge of the black hole completely disappears. For a charged black hole, the extremal black hole will technically not prevent and stop the evaporation anymore under charged Hawking radiation.