Gravitational Collapse in 1+1 Dimensions and Quantum Gravity

TL;DR

This paper explores the quantum aspects of 1+1 dimensional dilaton gravity, revealing new features in the measure and singularity structure, and discusses implications for black hole evaporation and information loss.

Contribution

It provides an explicit evaluation of the functional measures and derives Wheeler-DeWitt equations, highlighting differences from ADM formalism and analyzing singularities and quantum regions.

Findings

Singularity occurs at 4d = 4d (>0) with 4d related to matter fields.

Quantum region extends behind the singularity where the kinetic term's sign changes.

Disappearance of singularity when 4d < 0, indicating different quantum gravitational behaviors.

Abstract

We investigate the quantum theory of 1+1 dimensional dilaton gravity, which is an interesting toy model of the black hole dynamics. The functional measures of gravity part are explicitly evaluated and derive the Wheeler-DeWitt like equations as physical state conditions. In ADM formalism the measures are very ambiguous, but in our formalism they are explicitly defined. Then the new features which are not seen in ADM formalism come out. A singularity appears at $\df^2 =\kappa (>0) $, where $\kappa =(N-51/2)/12 $ and $ N$ is the number of matter fields. At the final stage of the black hole evaporation, the Liouville term becomes important, which just comes from the measures of the fields. Behind the singularity the quantum mechanical region $\kappa > \df^2 >0 $ extends, where the sign of the kinetic term in the Wheeler-DeWitt like equation changes. If $\kappa <0 $, the singularity disappears. We briefly discuss the possibility of gravitational tunneling and the issue of the information loss. (Talk given at "YITP Workshop on Theories of Quantum Fields -Beyond Perturbation-", Kyoto, Japan, 14-17 July 1992. Some misleading arguments in the preprint UT-Komaba 92-7 entitled "Quamtum Theory of Dilaton Gravity in 1+1 Dimensions" are corrected. The several remarks on the quantization are included. The difference from the other quantum theory is clarified.