Entropy in the Kerr - Newman black hole

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Abstract
The entropy of the Kerr - Newman black hole is calculated via the brick-wall method while paying careful attention to the contribution of superradiant scalar modes. It turns out that the nonsuperradiant and superradiant modes contribute simultaneously to the entropy with the same order in terms of the brick-wall cut-off . In particular, the contribution of the superradiant modes to the entropy is negative. To avoid divergence in this method when the angular velocity tends to zero, we propose to introduce 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 dependence structure of the brick-wall cut-off, which naturally requires an angular cut-off . Finally, if the cut-off values, and , satisfy a proper relation between them, the resulting entropy satisfies the area law.

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