Space-time Geometry in Exactly Solvable Quantum Dilaton Gravity

TL;DR

This paper rigorously derives space-time geometry in an exactly solvable quantum dilaton gravity model, demonstrating how matter configurations lead to black hole formation with or without naked singularities.

Contribution

It provides a detailed method to extract space-time geometry from an exactly solvable quantum dilaton gravity model using BRST formalism and coherent states.

Findings

Successfully computed mean values of stress-energy tensor and inverse metric.

Constructed states describing black hole formation from matter shock waves.

Demonstrated formation of black holes with and without naked singularities.

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.