THE ENERGY-DISTRIBUTION FOR A SPHERICALLY SYMMETRICAL ISOLATED SYSTEMIN GENERAL-RELATIVITY

The problems of the total energy and quasilocal energy density for an isolated spherically symmetric static system in general relativity (GR ) are considered with examples of some exact solutions. The field form ulation of GR developed earlier by L.P. Grishchuk, et al. (1984), in t he framework of which all the dynamical fields, including the gravitat ion field, are considered in a fixed background spacetime, is used int ensively. The exact Schwarzschild and Reissner-Nordstrom solutions are investigated in detail, and the results are compared with those in th e recent work by J.D. Brown and J.W. York, Jr. (1993) as well as discu ssed with respect to the principle of nonlocalization of the gravitati onal energy in GR. Those examples are illustrative and simple because the background is selected as Minkowski spacetime and, in fact, the fi eld configurations are studied in the framework of special relativity. It is shown that some problems of the Schwarzschild solution which ar e difficult to resolve in the standard geometrical framework of GR are resolved in the framework of the field formulation.