Abstract
We describe in detail how one can extract space-time geometry in an exactly solvable model of quantum dilaton gravity of the type propsoed by Callan, Giddings, Harvey, and Strominger (CGHS). Based on our previous work, in which a model with 24 massless matter scalars was quantized rigorously in the BRST operator formalism, we compute, without approximation, mean values of the matter stress-energy tensor, the inverse metric, and some related quantities in a class of coherent physical states constructed in a specific gauge within the conformal gauge. Our states are so designed as to describe a variety of space-time in which infalling matter energy distribution produces a black hole with or without a naked singularity. In particular, we have been able to produce the prototypical configuration first discovered by CGHS, in which a (smeared) matter shock wave produces a black hole without a naked singularity.
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