Information paradox in a Kerr-Newman black hole under generalized Hawking radiation

Abstract

Analogous to the calculation method of the interior volume inside a spherically symmetric black hole, we calculate the interior volume of a Kerr-Newman black hole. After that, we propose the generalized Stefan-Boltzmann law which can be used to investigate Hawking radiation with energy, charge and angular momentum. Based on it, the proportional relation between the entropy of the scalar field in the interior volume of the Kerr-Newman black hole and Bekenstein-Hawking entropy under generalized Hawking radiation has been investigated. Comparing to Hawking radiation without charge and angular momentum, we find that no matter the particles radiated from the black hole take charge and angular momentum or not, the two types of entropy remain the same proportional relation expression. Furthermore, the proportionality coefficient of the two types of entropy has been analyzed and discussed. It is found that the two types of entropy are approximately proportional to each other in an infinitesimal process except the late stage of Hawking radiation. Moreover, the proportional relation can degenerate to the Schwarzschild case when the charge and angular momentum of the black hole completely disappear. It illustrates that, for a Kerr-Newman black hole, different from Hawking radiation carrying only energy, the extremal black hole will technically not prevent and stop the evaporation anymore under generalized Hawking radiation, and the proportional relation obtained is applicable to investigate the evolution relation between the two types of entropy under an arbitrary Hawking radiation. Finally, based on the evolution of the proportional relation under generalized Hawking radiation, the black hole information paradox is brought up again and discussed more deeply.