CANONICAL VARIABLES AND QUASI-LOCAL ENERGY IN GENERAL-RELATIVITY

Recently Brown and York have devised a new method for defining quasilocal energy in general relativity. Their method employs a Hamilton-Jacobi analysis of an action functional for a spatially bounded spacetime M, and this analysis yields expressions for the quasilocal energy and momentum surface densities associated with the two-boundary B of a spacelike slice of such a spacetime. These expressions are essentially Arnowitt-Deser-Misner variables, but with canonical conjugacy defined with respect to the time history 3B of the two-boundary. These boundary ADM variables match previous variables which have arisen directly in the study of black hole thermodynamics. Further, a 'microcanonical' action which features fixed-energy boundary conditions has been introduced in related work concerning the functional-integral representation of the density of quantum states for such a bounded gravitational system. This paper introduces Ashtekar-type variables on the time history 3B of the two-boundary and shows that these variables lead to elegant alternative expressions for the quasilocal sur-face densities. In addition, it is demonstrated here that both the boundary ADM variables and the boundary Ashtekar-type variables can be incorporated into a larger framework by appealing to the tetrad-dependent Sparling differential forms. Finally, using these results and a tetrad action principle employed by Goldberg, this paper constructs two new tetrad versions of the microcanonical action.