Quantum Theory of Dilaton Gravity in 1+1 Dimensions

Abstract

We discuss the quantum theory of 1+1 dimensional dilaton gravity, which is an interesting model with analogous features to the spherically symmetric gravitational systems in 3+1 dimensions. The functional measures over the metrics and the dilaton field are explicitly evaluated and the diffeomorphism invariance is completely fixed in conformal gauge by using the technique developed in the two dimensional quantum gravity. We argue the relations to the ADM formalism. The physical state conditions reduce to the usual Wheeler-DeWitt equations when the dilaton $\df^2 ~ (=\e^{-2ϕ}) $ is large enough compared with $\kappa =(N-51/2)/12$, where $N$ is the number of matter fields. This corresponds to the large mass limit in the black hole geometry. A singularity appears at $\df^2 =κ(>0) $. The final stage of the black hole evaporation corresponds to the region $\df^2 \sim κ$, where the Liouville term becomes important, which just comes from the measure of the metrics. If $\kappa <0$, the singularity disappears.

15 pages. phyzzx. UT-Komaba 92-7

References in corpus (9)

• Evanescent Black Holes
• Are Horned Particles the Climax of Hawking Evaporation?
• Liouville Models of Black Hole Evaporation
• Quantization of a Theory of 2d Dilaton Gravity
• Evaporation of Two Dimensional Black Holes
• Hawking Radiation and Back-Reaction
• Fadeev-Popov Ghosts and 1+1 Dimensional Black Hole Evaporation
• Quantum Theories of Dilaton Gravity
• Quantum Black Holes

Cited by in corpus (19)

• Dilaton Gravity in Two Dimensions
• Quantum Theories of Dilaton Gravity
• Exact Operator Quantization of a Model of Two-Dimensional Dilaton Gravity
• 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
• Consequence of Hawking radiation from 2d dilaton black holes
• Semi-classical Approach to Charged Dilatonic Black Hole in Two Dimensions
• Quantum Fluctuations and Curvature Singularities in Jackiw-Teitelboim Gravity
• Physical States, Factorization and Nonlinear Structures in Two Dimensional Quantum Gravity
• Quantum Aspects of Black Holes
• Ghost-free infinite-derivative dilaton gravity in two dimensions
• Schwarzschild-de Sitter black hole in canonical quantization
• All Or Nothing: On the Small Fluctuations of Two-Dimensional String-Theoretic Black Holes
• Newtonian approximation in (1 + 1) dimensions
• Black Hole Physics from Two Dimensional Dilaton Gravity based on $SL(2,R)/U(1)$ Coset Model
• Ward Identities of W_{\infty} Symmetry and Higher Genus Amplitudes in 2D String Theory
• Gravitational Collapse in 1+1 Dimensions and Quantum Gravity