Black Hole Entropy from Horizon Conformal Field Theory

TL;DR

The paper proposes that black hole entropy is governed by a universal, horizon-based conformal symmetry rooted in classical general relativity, rather than the details of quantum gravity. By analyzing the Poisson structure of diffeomorphisms with a horizon boundary, it identifies a classical central extension and a Virasoro-like algebra whose central charge, together with the appropriate L0 eigenvalue, fixes the asymptotic density of states via Cardy’s formula, recovering the Bekenstein-Hawking entropy in higher dimensions. It argues that near-horizon physics reduces effectively to a two-dimensional conformal field theory, with potential realizations through horizon reductions (e.g., Liouville theory) or via boundary diffeomorphisms, suggesting a universal mechanism for black hole thermodynamics. The approach provides a bridge between horizon boundary conditions, conformal symmetry, and the entropy universal across quantum gravity frameworks, with extensions to other horizons and gravity theories, while leaving open technical issues on boundary prescriptions and dynamical evolution.

Abstract

String theory and ``quantum geometry'' have recently offered independent statistical mechanical explanations of black hole thermodynamics. But these successes raise a new problem: why should models with such different microscopic degrees of freedom yield identical results? I propose that the asymptotic behavior of the density of states at a black hole horizon may be determined by an underlying symmetry inherited from classical general relativity, independent of the details of quantum gravity. I offer evidence that a two-dimensional conformal symmetry at the horizon, with a classical central extension, may provide the needed behavior.