Canonical Variables and Quasilocal Energy in General Relativity
Abstract
Using the firstprinciples technique of Hamilton and Jacobi, Broandaad York have recently determined what geometric entities play the role of (quasilocal) energy in Einstein's theory of general relativity. They start from an action functional for a spatially bounded spacetime M, and their analysis yields expressions for the quasilocal energy and momentum surface densities associated with the twoboundary B of a spacelike hypersurface Sigma of such a spacetime. These expressions are essentially ArnowittDeserMisner variables, but with canonical conjugacy defined with respect to the time history { cal T} of the twoboundary. They match previous variables which have arisen directly in the study of blackhole thermodynamics and, furthermore, are the key ingredient in the construction of functionalintegral (quantum) partition functions which correspond to treating the (spatially bounded and selfgravitating) system Sigma in various statistical ensembles. This dissertation examines the role played by all possible types of canonical gravitational variables in the BrownYork theory of quasilocal energy. Among the variables considered are new Ashtekartype and new spinor type variables defined on the time history { cal T}, both of which lead to interesting alternative expressions for the quasilocal surface densities. The {cal T} Ashtekar variables enjoy all of the magical properties associated with the conventional Ashtekar variables. In particular, they allow for loworder polynomial expressions of the constraints associated with embedding {cal T} in the Einstein space M. Further, the {cal T} Ashtekar variables provide a compact expression for the boundary piece of the gravitational Hamiltonian, which modulo the constraints of the theory is the full Hamiltonian. This dissertation also thoroughly investigates the geometric features which appear in canonical triad gravity when the system Sigma possesses a boundary structure. The purpose of this dissertation is to lay the groundwork for a connection formulation of gravitational thermodynamics which will prove useful for future study of the quantum partition functions.
 Publication:

Ph.D. Thesis
 Pub Date:
 1994
 Bibcode:
 1994PhDT.......229L
 Keywords:

 GRAVITATIONAL;
 BLACK HOLE THERMODYNAMICS;
 Physics: General; Mathematics