Statistical Entropy of Three-dimensional Kerr-De Sitter Space

TL;DR

This paper analyzes the (2+1)-dimensional Kerr-De Sitter space, identifying phase transitions and computing its statistical entropy using Chern-Simons theory and extended Cardy's formula, aligning with thermodynamic predictions.

Contribution

It introduces a novel application of Chern-Simons theory and extended Cardy's formula to compute the statistical entropy of Kerr-De Sitter space, confirming thermodynamic consistency.

Findings

Identifies a phase transition at M^2=J^2/3l^2.

Finds a lower bound on the horizon temperature.

Computes entropy consistent with thermodynamics.

Abstract

I consider the (2+1)-dimensional Kerr-De Sitter space and its statistical entropy computation. It is shown that this space has only one (cosmological) event horizon and there is a phase transition between the stable horizon and the evaporating horizon at a point $M^2={1/3}J^2/l^2$ together with a lower bound of the horizon temperature. Then, I compute the statistical entropy of the space by using a recently developed formulation of Chern-Simons theory with boundaries, and extended Cardy's formula. This is in agreement with the thermodynamics formula.