Two Dimensional Quantum Dilaton Gravity and the Positivity of Energy

Abstract

Using an argument due to Regge and Teitelboim, an expression for the ADM mass of 2d quantum dilaton gravity is obtained. By evaluating this expression we establish that the quantum theories which can be written as a Liouville-like theory, have a lower bound to energy, provided there is no critical boundary. This fact is then reconciled with the observation made earlier that the Hawking radiation does not appear to stop. The physical picture that emerges is that of a black hole in a bath of quantum radiation. We also evaluate the ADM mass for the models with RST boundary conditions and find that negative values are allowed. The Bondi mass of these models goes to zero for large retarded times, but becomes negative at intermediate times in a manner that is consistent with the thunderpop of RST.

16 pages, phyzzx, COLO-HEP-309. (Confusing points in previous version clarified, discussion of ADM and Bondi masses in RST case added.)

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• The Endpoint of Hawking Evaporation
• Are Horned Particles the Climax of Hawking Evaporation?
• Black Hole Evaporation in 1+1 Dimensions
• Liouville Models of Black Hole Evaporation
• Cosmic Censorship in Two-Dimensional Gravity
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• Quantum Black Holes in Two Dimensions
• Black Hole Physics from Liouville Theory
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Cited by in corpus (9)

• Energy-Momentum Conservation in General Relativity
• Black Hole Entropy in Two Dimensions
• Nonsingular Black Hole Evaporation and ``Stable'' Remnants
• The Problem of Time and Quantum Black Holes
• Hawking Radiation and Evaporation of the Black Hole Induced by a Klein-Gordon Soliton
• Diffeomorphisms, Noether Charges and Canonical Formalism in 2D Dilaton Gravity
• 2D quantum dilaton gravitational Hamiltonian, boundary terms and new definition for total energy
• Black Hole Physics from Two Dimensional Dilaton Gravity based on $SL(2,R)/U(1)$ Coset Model
• Quantum-Corrected Bondi Mass for 2D Hawking Radiation