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 ${\mathcal{I}}^{-}$ 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

3 pages no figures

References in corpus (2)

• Horizon constraints and black hole entropy
• Horizon Constraints and Black Hole Entropy

Cited by in corpus (7)

• Entropy and Temperature From Black-Hole/Near-Horizon-CFT Duality
• A Near Horizon CFT Dual for Kerr-Newman-$AdS$
• Evaporation and information puzzle for 2D nonsingular asymptotically flat black holes
• Black Hole Entropy and the Problem of Universality
• Thermodynamics of nonspherical black holes from Liouville theory
• On the Near Horizon Canonical Quantum Microstates from $Ad{S}_2/CF{T}_1$ and Conformal Weyl Gravity
• Nöther Currents, Black Hole Entropy Universality and CFT Duality in Conformal Weyl Gravity