Energy and momentum in general relativity - III. The total energy, momentum and angular momentum of an isolated finite system generating gravitational waves

Abstract

The theory of energy and momentum developed by the author is applied to the solution for the metric field obtained by Sachs for an isolated bounded source generating gravitational waves in space-time which is asymptotically flat. Expressions are found for the total 4-momentum and angular momentum of the field and source. The total energy agrees with the expression identified by Sachs as the mass of the system. Both the flux of 4-momentum and the flux of angular momentum to infinity are determined by a single complex function of three variables, and they both vanish when the time derivative of this function is zero (no news). Within the group of allowed transformations discussed by Sachs the 4-momentum flux to infinity is given uniquely.