Mixture of outgoing and incoming gravitational radiation: change of mass of the source of radiation

Abstract

It has been fairly well established theoretically in recent works that outward travelling spherical gravitational waves carry away energy from their source. Methods of successive approximations applied to the Einstein gravitational field equations of general relativity have been used for that purpose. The object of this paper is to show, by a double-series approximation method, a similar result for the general case of any mixture of outgoing and incoming radiation.