Liouville lost, Liouville regained: central charge in a dynamical background

Several recent approaches to black hole entropy obtain the density of state s from the central charge of a Liouville theory. If Liouville theory is cou pled to a dynamical spacetime background, however, the classical central ch arge vanishes. I show that the central charge can be restored by introducin g appropriate constraints, which may be interpreted ax fall-off conditions at a boundary such as a black hole horizon. (C) 2001 Published by Elsevier Science B.V.