Entropy from Conformal Field Theory at Killing Horizons

TL;DR

The paper proposes that black hole entropy can be derived from horizon-boundary symmetries without detailed knowledge of quantum gravity. By covariantly extending the constraint algebra at a horizon, a Virasoro structure with a calculable central charge emerges, enabling Cardy-state counting to reproduce the Bekenstein-Hawking entropy across diverse spacetimes. This suggests a universal, symmetry-based statistical-mechanical account of horizon thermodynamics, with extensions to other gravity theories and dynamical horizons. The work also highlights technical subtleties around boundary conditions and the precise applicability of the Cardy formula in nonstandard setups.

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.