Horizon constraints and black hole entropy

TL;DR

This paper demonstrates that imposing horizon constraints in quantum gravity modifies the symmetry algebra at the horizon, enabling the use of conformal field theory techniques to derive black hole entropy consistent with Bekenstein-Hawking results.

Contribution

It introduces a method to incorporate horizon constraints that alter symmetry algebras, providing a microscopic explanation for black hole entropy in 2D dilaton gravity.

Findings

Horizon constraints induce a central extension in the symmetry algebra.

Conformal field theory methods reproduce the Bekenstein-Hawking entropy.

Microscopic states are identified as 'would-be pure gauge' states made physical by horizon conditions.

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 as well, the imposition of a "stretched horizon" constraint alters the algebra of symmetries at the horizon, introducing a central term. Standard conformal field theory techniques can then then be used to obtain the asymptotic density of states, reproducing the Bekenstein-Hawking entropy. The microscopic states responsible for black hole entropy can thus be viewed as "would-be pure gauge" states that become physical because the symmetry is altered by the requirement that a horizon exist.