Horizon Constraints and Black Hole Entropy

TL;DR

This paper demonstrates how imposing horizon constraints in 2D dilaton gravity modifies symmetry algebras, leading to a conformal field theory approach that reproduces black hole entropy via boundary states.

Contribution

It shows that horizon constraints alter symmetry algebras, enabling a CFT-based derivation of black hole entropy in 2D gravity.

Findings

Horizon constraints induce a central extension in symmetry algebra.

The modified algebra allows counting of states matching Bekenstein-Hawking entropy.

Black hole entropy can be understood through boundary states as 'would-be gauge' states.

Abstract

To ask a question about a black hole in quantum gravity, one must restrict initial or boundary data to ensure that a black hole is actually present. For two-dimensional dilaton gravity, and probably a much wider class of theories, I show that the imposition of a spacelike ``stretched horizon'' constraint modifies the algebra of symmetries, inducing a central term. Standard conformal field theory techniques then fix the asymptotic density of states, reproducing the Bekenstein-Hawking entropy. The states responsible for black hole entropy can thus be viewed as ``would-be gauge'' states that become physical because the symmetries are altered.