Entropy in the Kerr-Newman Black Hole

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 $ε$. 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 $θ$-dependence structure of the brick wall cutoff, which natu rally requires an angular cutoff $δ$. Finally, if the cutoff values, $ε$ and $δ$, satisfy a proper relation between them, the resulting entropy satisfies the area law.