Statistical Mechanics on Axially-symmetric Space-times with the Killing Horizon and Entropy of Rotating Black Holes in Induced Gravity

TL;DR

This paper introduces a method to compute the free-energy of quantum fields near rotating black hole horizons, showing that entropy divergences are similar to static cases and that black hole entropy in induced gravity is rotation-independent.

Contribution

It develops a universal reduction technique relating stationary and static backgrounds, simplifying the analysis of quantum fields near rotating black holes and their entropy.

Findings

Entropy divergences are identical to static cases and renormalizable.

Black hole entropy in induced gravity is rotation-independent.

The reduction simplifies statistical mechanics calculations for rotating black holes.

Abstract

We develop a method for computing the free-energy of a canonical ensemble of quantum fields near the horizon of a rotating black hole. We show that the density of energy levels of a quantum field on a stationary background can be related to the density of levels of the same field on a fiducial static space-time. The effect of the rotation appears in the additional interaction of the "static" field with a fiducial abelian gauge-potential. The fiducial static space-time and the gauge potential are universal, i.e., they are determined by the geometry of the given physical space-time and do not depend on the spin of the field. The reduction of the stationary axially symmetric problem to the static one leads to a considerable simplification in the study of statistical mechanics and we use it to draw a number of conclusions. First, we prove that divergences of the entropy of scalar and spinor fields at the horizon in the presence of rotation have the same form as in the static case and can be removed by renormalization of the bare black hole entropy. Second, we demonstrate that statistical-mechanical representation of the Bekenstein-Hawking entropy of a black hole in induced gravity is universal and does not depend on the rotation.