Boundary Conditions and Quasilocal Energy in the Canonical Formulation of All 1+1 Models of Gravity

Abstract

Within a first-order framework, we comprehensively examine the role played by boundary conditions in the canonical formulation of a completely general two-dimensional gravity model. Our analysis particularly elucidates the perennial themes of mass and energy. The gravity models for which our arguments are valid include theories with dynamical torsion and so-called generalized dilaton theories (GDTs). Our analysis of the canonical action principle (i) provides a rigorous correspondence between the most general first-order two-dimensional Einstein-Cartan model (ECM) and GDT and (ii) allows us to extract in a virtually simultaneous manner the ``true degrees of freedom'' for both ECMs and GDTs. For all such models, the existence of an absolutely conserved (in vacuo) quantity C is a generic feature, with (minus) C corresponding to the black-hole mass parameter in the important special cases of spherically symmetric four-dimensional general relativity and standard two-dimensional dilaton gravity. The mass C also includes (minimally coupled) matter into a ``universal mass function.'' We place particular emphasis on the (quite general) class of models within GDT possessing a Minkowski-like groundstate solution (allowing comparison between $C$ and the Arnowitt-Deser-Misner mass for such models).

REVTeX, 41 pages, 2 Postscript figures, 10 macros

References in corpus (2)

• String Model with Dynamical Geometry and Torsion
• The reduced phase space of spherically symmetric Einstein-Maxwell theory including a cosmological constant

Cited by in corpus (10)

• Dilaton Gravity in Two Dimensions
• Target-Superspace in 2d Dilatonic Supergravity
• Quantization of the String Inspired Dilaton Gravity and the Birkhoff Theorem
• Generalized 2d dilaton gravity with matter fields
• Universal conservation law and modified Noether symmetry in 2d models of gravity with matter
• Constraint Lie algebra and local physical Hamiltonian for a generic 2D dilatonic model
• On static solutions in 2D dilaton gravity with scalar matter
• Energy for N-Body Motion in Two Dimensional Gravity
• Physics-to-gauge conversion at black hole horizons
• A note on dilaton gravity with non-smooth potentials