Black Hole Thermodynamics from Euclidean Horizon Constraints

TL;DR

The paper argues that near-horizon physics of a broad class of black holes is governed by a two-dimensional conformal field theory arising from horizon constraints in Euclidean dilaton gravity. By imposing a stretched-horizon constraint and using a Bergmann-Komar construction, a Virasoro algebra with a calculable central charge is obtained, enabling entropy counting via Cardy’s formula, which reproduces the Bekenstein-Hawking result up to a universal $2\pi$ factor. The BTZ and other string-theory motivated black holes are shown to be special cases of this horizon-conformal picture, supporting a universal mechanism for black hole entropy that does not rely on specific microphysics. The entropy interpretation is tied to Goldstone-boson-like horizon modes resulting from the conformal anomaly, with prospects for coupling to Hawking radiation and implications for a unified quantum gravity description.

Abstract

To explain black hole thermodynamics in quantum gravity, one must introduce constraints to ensure that a black hole is actually present. I show that for a large class of black holes, such ``horizon constraints'' allow the use of conformal field theory techniques to compute the density of states, reproducing the Bekenstein-Hawking entropy in a nearly model-independent manner. One standard string theory approach to black hole entropy arises as a special case, lending support to the claim that the mechanism may be ``universal.'' I argue that the relevant degrees of freedom are Goldstone-boson-like excitations arising from the weak breaking of symmetry by the constraints.