On the Entropy of a Quantum Field in the 2 + 1 Dimensional Spinning Black Holes

TL;DR

This paper computes the entropy of a scalar field in a 2+1 dimensional rotating black hole, revealing divergence behavior and the impact of superradiant modes, with implications for black hole thermodynamics.

Contribution

It provides a detailed calculation of scalar field entropy in 2+1D rotating black holes, highlighting divergence patterns and mode contributions.

Findings

Entropy is proportional to horizon area in Hartle-Hawking state.

Entropy diverges linearly with the square root of the radial cutoff.

Superradiant modes do not contribute to entropy in WKB approximation.

Abstract

We calculate the entropy of a scalar field in a rotating black hole in 2 + 1 dimension. In the Hartle-Hawking state the entropy is proportional to the horizon area, but diverges linearly in $\sqrt{h}$, where $h$ is the radial cut-off. In WKB approximation the superradiant modes do not contribute to the entropy.