A NEW PHASE FOR GENERAL-RELATIVITY

The author studies Ashtekar's formulation (1988) of general relativity, restricted to spherically symmetric field configurations. The author solves the constraint equations for all metrics that are degenerate throughout the foliating hypersurface. Three sets of boundary conditions are discussed with some care. The first set is the conventional one, used in the asymptotically flat case. The second is the set of boundary conditions that would normally be imposed on SO(3) Yang-Mills theory; then, the correct Hamiltonian is a linear combination of constraints. A slightly modified set of boundary conditions allows the author to set the Hamiltonian weakly equal to an SO(3) charge, while the charges corresponding to energy and momentum are ill-defined or vanishing. In other words, it is suggested that there is a 'phase' of general relativity in which the metric is degenerate, energy is an ill-defined concept, and its role is taken over by SO(3) charges.