Statistical entropy of three-dimensional Kerr–de Sitter space

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 M2=13J2/l2 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 the Chern–Simons theory with boundaries, and extended Cardyʹs formula. This is in agreement with the thermodynamics formula.