Entropy from Conformal Field Theory at Killing Horizons

TL;DR

This paper demonstrates that conformal field theory techniques applied to Killing horizons in various spacetimes can derive black hole entropy, showing that symmetry principles alone can determine the Bekenstein-Hawking entropy without detailed quantum gravity models.

Contribution

It establishes a method to compute black hole entropy using boundary conformal symmetry at Killing horizons across different spacetime geometries.

Findings

Density of states matches Bekenstein-Hawking entropy

Virasoro algebra with calculable central charge at horizons

Entropy derived independently of quantum gravity details

Abstract

On a manifold with boundary, the constraint algebra of general relativity may acquire a central extension, which can be computed using covariant phase space techniques. When the boundary is a (local) Killing horizon, a natural set of boundary conditions leads to a Virasoro subalgebra with a calculable central charge. Conformal field theory methods may then be used to determine the density of states at the boundary. I consider a number of cases---black holes, Rindler space, de Sitter space, Taub-NUT and Taub-Bolt spaces, and dilaton gravity---and show that the resulting density of states yields the expected Bekenstein-Hawking entropy. The statistical mechanics of black hole entropy may thus be fixed by symmetry arguments, independent of details of quantum gravity.