  We study the relation between the $SL(2,R)/U(1)$ black hole and the $c=1$
Liouville theory. A deformation, which interpolates the BRST operators of both
models, is explicitly constructed. This interpolation is isomorphic, and the
physical spectrum of the black hole is equivalent to that of the $c=1$ model
tensored by a topological $U(1)/U(1)$ model. Some implications of the
deformation are discussed.
