Statistical Mechanics of Three-dimensional Kerr-de Sitter Space

TL;DR

This paper computes the entropy of three-dimensional Kerr-de Sitter space using a gauge degrees of freedom approach, resolving previous issues with boundary conditions and unproven formulas, and aligns with the Bekenstein-Hawking entropy.

Contribution

It demonstrates that the entropy can be derived without relying on the infinite boundary or Cardy's formula, providing a consistent method for de Sitter space.

Findings

Entropy matches Bekenstein-Hawking value

No need for boundary at infinity

Avoids unproven assumptions in previous methods

Abstract

The statistical computation of the (2+1)-dimensional Kerr-de Sitter space in the context of the {\it classical} Virasoro algebra for an asymptotic isometry group has been a mystery since first, the degeneracy of the states has the right value only at the infinite boundary which is casually disconnected from our universe, second, the analyses were based on the unproven Cardy's formula for complex central charge and conformal weight. In this paper, I consider the entropy in Carlip's "would-be gauge" degrees of freedom approach instead. I find that it agree with the Bekenstein-Hawking entropy but there are no the above problems. Implications to the dS/CFT are noted.