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

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

1998-06-30

arxiv.org/abs/gr-qc/9806118v2

Phys.Lett. B445 (1998) 27-35

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

13 pages, plain latex, no figure, version published in Phys. Lett. B, Emphasis is given on the quantization of superradiance m

Scientific paper

10.1016/S0370-2693(98)01451-8

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.

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