The relativity theory of divergent waves

Einstein investigated the problem of the propagation of gravitational waves in 1916 and 1918. The special case of plane waves of small amplitude was considered by Weyl, who showed that such waves may be regarded as the result of superposing weaves of three types. Eddington found that of these only one, the transverse-transverse, is real, and identified a particular type of electromagnetic transverse-transverse wave with light. The gravitational potentials in his solution, however, contain an aperiodic term which increases without limit, from which it is inferred that light cannot be propagated indefinitely either in space or time. We considered the case of plane waves of finite amplitude and came to the conclusion that an infinite plane electromagnetic wave cannot be propagated without change of wave-form, and suggested that the relativity theory of light must be approached by way of the study of divergent waves. The present discussion is confined to waves of a purely gravitational nature.