Statistical Entropy of Three-dimensional Kerr-De Sitter Space

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.