Hamiltonian Approach to 2D Dilaton-Gravities and Invariant Adm Mass

Abstract

The formula existing in the literature for the ADM mass of 2D dilaton gravity is incomplete. For example, in the case of an infalling matter shockwave this formula fails to give a time-independent mass, unless a very special coordinate system is chosen. We carefully carry out the canonical formulation of 2D dilaton gravity theories (classical, CGHS and RST). As in 4D general relativity one must add a boundary term to the bulk Hamiltonian to obtain a well-defined variational problem. This boundary term coincides with the numerical value of the Hamiltonian and gives the correct mass which obviously is time-independent.

revised, 12 pages, PUPT-1379; we added a reference and corrected some minor typos

References in corpus (9)

• Evanescent Black Holes
• The Endpoint of Hawking Evaporation
• Liouville Models of Black Hole Evaporation
• Cosmic Censorship in Two-Dimensional Gravity
• Quantization of a Theory of 2d Dilaton Gravity
• Hawking Radiation and Back-Reaction
• Black Hole Physics from Liouville Theory
• Supersymmetry and Positive Energy in Classical and Quantum Two-Dimensional Dilaton Gravity
• Positive Energy Theorem and Supersymmetry in Exactly Solvable Quantum-Corrected 2D Dilaton-Gravity

Cited by in corpus (29)

• Energy-Momentum Conservation in General Relativity
• Semi-infinite Throat as the End-state Geometry of two-dimensional Black Hole Evaporation
• Black Hole Information
• Conserved Quasilocal Quantities and General Covariant Theories in Two Dimensions
• A Non-Singular Black Hole
• Towards complete integrability of two dimensional Poincaré gauge gravity
• Nonsingular Black Hole Evaporation and ``Stable'' Remnants
• Solvable Models for radiating Black Holes and Area-preserving Diffeomorphisms
• Classical and quantum geometrodynamics of 2d vacuum dilatonic black holes
• Unitary Theory of Evaporating 2D Black Holes
• Predictability and Semiclassical Approximation at the onset of Black Hole formation
• Hamiltonian thermodynamics of two-dimensional vacuum dilatonic black holes
• Two Dimensional Quantum Dilaton Gravity and the Positivity of Energy
• Positive Energy Theorem and Supersymmetry in Exactly Solvable Quantum-Corrected 2D Dilaton-Gravity
• Accelerating universe in two-dimensional noncommutative dilaton cosmology
• ADM mass of the quantum-corrected Schwarzchild black hole
• Transition from AdS universe to DS universe in the BPP model
• A solution to the zero-hamiltonian problem in 2-D gravity
• An effective Hamiltonian for 2D black hole Physics
• 2D quantum dilaton gravitational Hamiltonian, boundary terms and new definition for total energy
• Future singularity free accelerating expansion with the modified Poisson brackets
• Cosmological Constant Seesaw in String/M-Theory
• Diffeomorphisms, Noether Charges and Canonical Formalism in 2D Dilaton Gravity
• The No-Hair Conjecture in 2D Dilaton Supergravity
• Baby universes and energy (non-)conservation in (1+1)-dimensional dilaton gravity
• Canonical Structure of 2D Black Holes
• Two non-commutative parameters and regular cosmological phase transition in the semi-classical dilaton cosmology
• 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