Entropy in the Kerr-Newman Black Hole

TL;DR

This paper calculates the entropy of Kerr-Newman black holes using the brick wall method, accounting for superradiant modes, and finds conditions under which the entropy obeys the area law.

Contribution

It introduces a new approach to handle superradiant modes and angular velocity bounds in the brick wall method for Kerr-Newman black holes.

Findings

Superradiant modes contribute negatively to entropy.

A lower bound on angular velocity is proposed to prevent divergences.

Proper relation between cutoff parameters ensures entropy follows the area law.

Abstract

Entropy of the Kerr-Newman black hole is calculated via the brick wall method with maintaining careful attention to the contribution of superradiant scalar modes. It turns out that the nonsuperradinat and superradiant modes simultaneously contribute to the entropy with the same order in terms of the brick wall cutoff $\epsilon$. In particular, the contribution of the superradiant modes to the entropy is negative. To avoid divergency in this method when the angular velocity tends to zero, we propose to intr oduce a lower bound of angular velocity and to treat the case of the angular momentum per unit mass $a=0$ separately. Moreover, from the lower bound of the angular velocity, we obtain the $\theta$-dependence structure of the brick wall cutoff, which natu rally requires an angular cutoff $\delta$. Finally, if the cutoff values, $\epsilon$ and $\delta$, satisfy a proper relation between them, the resulting entropy satisfies the area law.