Statistical entropy of the Schwarzschild black hole

TL;DR

This paper derives the statistical entropy of the Schwarzschild black hole by linking asymptotic symmetries at null infinity to a conformal field theory, confirming the Bekenstein-Hawking entropy via holographic principles.

Contribution

It introduces a novel approach connecting asymptotic symmetries near null infinity to a boundary conformal field theory, deriving black hole entropy from a Virasoro algebra and Cardy's formula.

Findings

Successfully reproduces Bekenstein-Hawking entropy using conformal field theory methods.

Establishes a link between asymptotic symmetries and holographic entropy calculations.

Supports a non-local holographic realization of black hole thermodynamics.

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