BOUNDARY-CONDITIONS AND QUASI-LOCAL ENERGY IN THE CANONICAL FORMULATION OF ALL 1-MODELS OF GRAVITY(1)

Within a first-order framework, we comprehensively examine the role pl ayed by boundary conditions in the canonical formulation of a complete ly general two-dimensional gravity model. Our analysis particularly el ucidates the perennial themes of mass and energy. The gravity models f or which our arguments are valid include theories with dynamical torsi on 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 m odel (ECM) and GDT and (ii) allows us to extract in a virtually simult aneous manner the ''true degrees of Freedom'' for both ECMs and GDTs. For all such models, the existence of an absolutely conserved (in vacu o) quantity C is a generic feature, with (minus) C corresponding to th e black-hole mass parameter in the important special cases of spherica lly symmetric four-dimensional general relativity and standard two-dim ensional dilaton gravity. The mass C also includes (minimally coupled) matter into a ''universal mass function.'' We place particular emphas is on the (quite general) class of models within GDT possessing a Mink owski-like groundstate solution (allowing comparison between C and the Arnowitt-Deser-Misner mass for such models). (C) 1997 Academic Press.