Four-Dimensional Entropy from Three-Dimensional Gravity

Abstract

At the horizon of a black hole, the action of (3+1)-dimensional loop quantum gravity acquires a boundary term that is formally identical to an action for three-dimensional gravity. I show how to use this correspondence to obtain the entropy of the (3+1)-dimensional black hole from well-understood conformal field theory computations of the entropy in (2+1)-dimensional de Sitter space.

8 pages; v2: more references, typos fixed, minor rewording; v3: some clearer explanations in response to referees, more references