Recently, several solutions of the field equations of general relativity theory have been published which are based upon the Einstein-Infeld-Hoffmann approximation method and claim to represent radiative effects in the motion of freely gravitating particles. These solutions are analyzed and it is shown that none produced to date represents a satisfactory discussion of the possibility of radiation by freely gravitating particles.

The problem of the possibility of gravitational radiation by free particles is then investigated upon general grounds. It is shown that the possibility of such radiation depends on the definition of free particles. This definition depends on the (unproven) assumption that the Einstein-Infeld-Hoffmann method is, in its physical outcome, independent of the coordinate system. If this assumption were not true, this would constitute a severe limitation of the method and imply that all results have to be expressed in a standard coordinate system. Under these circumstances, the definition of free particles is obviously equivalent to a postulate of absence of radiation.

• Received 19 April 1955

DOI:https://doi.org/10.1103/PhysRev.99.1883