Superradiance and the Statistical-Mechanical Entropy of Rotating BTZ Black Holes

TL;DR

This paper accurately incorporates superradiant modes into the statistical-mechanical entropy calculation for rotating BTZ black holes, correcting previous errors and aligning the total entropy with the Bekenstein-Hawking entropy using a universal cutoff.

Contribution

It provides a corrected and comprehensive treatment of superradiant modes in the entropy calculation for rotating black holes, resolving past inaccuracies.

Findings

Superradiant mode contribution is positive and diverges similarly to nonsuperradiant modes.

Correct quantization of superradiant modes eliminates previous errors.

Total entropy matches Bekenstein-Hawking entropy with a universal cutoff.

Abstract

We have considered the divergence structure in the brick-wall model for the statistical mechanical entropy of a quantum field in thermal equilibrium with a black hole which {\it rotates}. Especially, the contribution to entropy from superradiant modes is carefully incorporated, leading to a result for this contribution which corrects some previous errors in the literature. It turns out that the previous errors were due to an incorrect quantization of the superradiant modes. Some of main results for the case of rotating BTZ black holes are that the entropy contribution from superradiant modes is positive rather than negative and also has a leading order divergence as that from nonsuperradiant modes. The total entropy, however, can still be identified with the Bekenstein-Hawking entropy of the rotating black hole by introducing a universal brick-wall cutoff. Our correct treatment of superradiant modes in the ``angular-momentum modified canonical ensemble'' also removes unnecessary introductions of regulating cutoff numbers as well as ill-defined expressions in the literature.