On electromagnetic and gravitational waves in general relativity. I

In this paper the external field of a bounded source emitting electromagnetic and gravitational radiation has been considered. The field has been assumed to be axially symmetric as well as reflexion symmetric and that it tends to flatness at infinity. The form of the electromagnetic tensor which is in accordance with the classical harmonic electric dipole radiation has been assumed. It has been shown that the whole set of field equations falls into seven main equations together with three supplementary conditions. These field equations have been solved by multipole expansion method and the corresponding Initial Value Problem has been discussed.