Quantum Gravity and Black Hole Dynamics in 1+1 Dimensions

Abstract

We study the quantum theory of 1+1 dimensional dilaton gravity, which is an interesting toy model of the black hole dynamics. The functional measures are explicitly evaluated and the physical state conditions corresponding to the Hamiltonian and the momentum constraints are derived. It is pointed out that the constraints form the Virasoro algebra without central charge. 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 =κ(>0) $, where $\kappa =(N-51/2)/12$ and $N$ is the number of matter fields. Behind the singularity the quantum mechanical region $κ> \df^2 >0 $ extends, where the sign of the kinetic term in the Hamiltonian constraint changes. If $\kappa <0$, the singularity disappears. We discuss the quantum dynamics of black hole and then give a suggestion for the resolution of the information loss paradox. We also argue the quantization of the spherically symmetric gravitational system in 3+1 dimensions. In appendix the differences between the other quantum dilaton gravities and ours are clarified and our status is stressed.

phyztex, UT-Komaba 92-14. A few misleading sentences are corrected and some references are added

Cited by in corpus (11)

• Dilaton Gravity in Two Dimensions
• Covariant Effective Action and One-Loop Renormalization of 2D Dilaton Gravity with Fermionic Matter
• Background-metric Independent Formulation of 4D Quantum Gravity
• A Unified Approach to Solvable Models of Dilaton Gravity in Two-Dimensions Based on Symmetry
• Dilaton Gravity in $2+\epsilon$ Dimensions
• Space-time Geometry in Exactly Solvable Quantum Dilaton Gravity
• Physical States, Factorization and Nonlinear Structures in Two Dimensional Quantum Gravity
• Ghost-free infinite-derivative dilaton gravity in two dimensions
• Dilaton-Maxwell gravity with matter near two dimensions
• Ward Identities of W_{\infty} Symmetry and Higher Genus Amplitudes in 2D String Theory
• Black Hole Physics from Two Dimensional Dilaton Gravity based on $SL(2,R)/U(1)$ Coset Model