Space-time geometry in exactly solvable quantum dilaton gravity

Abstract

We describe in detail how one can extract space-time geometry in an exactly solvable model of quantum dilaton gravity of the type proposed 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 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 in-falling matter energy distribution produces a black hole with or without naked sigularity. 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 naked sigularity. †

Baby universes and energy (non)conservation in (1+1)-dimensional dilaton gravity

“…and similarly forL 0 andL m , where α (±) m = α 0 m ± α 1 m . Equation (25) shows that the model is equivalent to the string with background charge [22,23,24,25] or, in other words, to the bosonic string in linear Dilaton background [20,21] Φ(x) = γ(e µ x µ ) = γx (+) (26) with e µ = (−1, 1, 0, . .…”

“…The DDF operators (28) are similar to those introduced in ref. [25]. Another choice of DDF operators in this model has been considered in refs.…”

“…In section 3 we outline the quantum version of this model, which is known for some time (see, e.g., refs. [22,23,24,25]), construct the states of parent universes (DDF states) and vertex operators corresponding to the emission of baby universes. Section 4 contains the main results of this paper.…”