SPACE-TIME GEOMETRY IN EXACTLY SOLVABLE QUANTUM DILATON GRAVITY

We describe in detail how one can extract space-time geometry in an ex actly solvable model of quantum dilaton gravity of the type proposed b y Callan, Giddings, Harvey, and Strominger (CGHS). Based on our previo us work, in which a model with 24 massless matter scalars was quantize d rigorously in the BRST operator formalism, we compute, without appro ximation, mean values of the matter stress-energy tenser, the inverse metric, and some related quantities in a class of coherent physical st ates constructed in a specific gauge within the conformal gauge. Our s tates are so designed as to describe a variety of space-time in which infalling matter energy distribution produces a black hole with or wit hout a naked singularity. In particular, we have been able to produce the prototypical configuration first discovered by CGHS, in which a (s meared) matter shock wave produces a black hole without a naked singul arity.