Hawking radiation with angular momentum and the entropy variation in a Kerr black hole

Abstract

Considering Hawking radiation with angular momentum, we propose a modified Stefan-Boltzmann law about the particles with both energy and angular momentum radiated from a Kerr black hole. Based on the modified Stefan-Boltzmann law, we calculate the entropy in the interior volume of the Kerr black hole and investigate the proportional relation between the variation of this entropy and the variation of Bekenstein-Hawking entropy under Hawking radiation. Comparing to Hawking radiation without angular momentum, we find that whether the particles radiated from the black hole take angular momentum cannot affect the proportional relation between the two types of entropy. Furthermore, the proportionality coefficient of the two types of entropy is investigated. It is found that this coefficient is approximately a constant except the late stage of Hawking radiation. Moreover, the proportional relation can degenerate to the Schwarzschild case when the angular momentum of the black hole completely disappears. For a Kerr black hole, the extremal black hole can technically not prevent and stop the evaporation anymore under Hawking radiation with angular momentum.

Volume dependent extension of Kerr-Newman black hole thermodynamics

“…Some authors have given only approximate evaluations of Kerr and Kerr-Newman black holes [17,18]. Also, while there are qualitative investigations about the Hawking radiation with angular momentum [28,29], there is an ambiguity in the evaporation process of rotating black holes because we do not know how much angular momentum can be emitted. This also must depend on the polarization of the radiation.…”

“…These investigations, however, mainly consider the contribution of a hypothetic scalar field, filling the interior volume, to the Bekenstein-Hawking result. The proportionality relations between the entropy of the scalar field in the interior volume of rotating black holes and the Bekenstein-Hawking entropy under the Hawking radiation, generalized by considering the particles with energy, charge and angular momentum was also investigated recently in [28,29].…”

Information evolution in the interior of an axially symmetric BTZ black hole

“…Its maximum value for other than Schowarzschild black hole can be easily evaluated by numerical method for detail see Ref. [13,35]. From this equation, the interior volume of black hole will be maximum for r = r v , which we labeled as maximal hyper-surface ranging form r − < r < r + and could be obtained by the maximization of polynomial −r 2 v f (r v ) as…”

Information paradox and corrected thermodynamics for black holes

“…where we have used the assumption ṪB ∼ 0 (26) in the first line, which means that the radiation process is slow [45,46], the first law of the black hole (6) was considered in the second line. Note that the approximation here is only suitable for the black hole with large mass.…”