Four-Dimensional Entropy from Three-Dimensional Gravity

TL;DR

This paper establishes a novel connection between four-dimensional black hole entropy and three-dimensional gravity, enabling entropy calculation via conformal field theory methods originally developed for lower-dimensional models.

Contribution

It introduces a method to derive four-dimensional black hole entropy from three-dimensional gravity boundary terms using conformal field theory techniques.

Findings

Derived four-dimensional black hole entropy from three-dimensional gravity

Established a formal correspondence between (3+1)D and (2+1)D gravity boundary actions

Demonstrated the use of conformal field theory in higher-dimensional black hole entropy calculations

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.