Statistical entropy of the Schwarzschild black hole

Abstract

We derive the statistical entropy of the Schwarzschild black hole by considering the asymptotic symmetry algebra near the $\cal{I^{-}}$ boundary of the spacetime at past null infinity. Using a two-dimensional description and the Weyl invariance of black hole thermodynamics this symmetry algebra can be mapped into the Virasoro algebra generating asymptotic symmetries of anti-de Sitter spacetime. Using lagrangian methods we identify the stress-energy tensor of the boundary conformal field theory and we calculate the central charge of the Virasoro algebra. The Bekenstein-Hawking result for the black hole entropy is regained using Cardy's formula. Our result strongly supports a non-local realization of the holographic principle