Horizon constraints and black-hole entropy

Abstract

A question about a black hole in quantum gravity is a conditional question: to obtain an answer, one must restrict initial or boundary data to ensure that a black hole is actually present. For two-dimensional dilaton gravity—and probably for 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, successfully 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.