Theorem on Nonradiative Electromagnetic and Gravitational Fields

Abstract

A vacuum electromagnetic field is considered which is (a) stationary below a hypersurface Σ intersecting all parametric lines of the time coordinate t and (b) nonradiative above Σ. It is proved that such a field is stationary also above Σ. The same theorem is proved to be valid for the pure gravitational field in general relativity and for the combined gravitational and electromagnetic field in the Einstein—Maxwell theory.