The gravitational field of a radiating electromagnetic dipole

The principle purpose of this paper is to analyze in the context of general relativity the effects of electromagnetic radiation on a gravitational field. The basic outline is that we start from flat-space with a time-dependent electric and magnetic dipole solution of Maxwell's equations. This field, treated as first order, then acts as the source for a gravitational perturbation. First, from the flat-space version of the Bianchi identities, with the Maxwell stress tensor as the (second-order) source, the Weyl tensor is found as a field on the Minkowski background. From this Weyl tensor, we go on and find the spin coefficients and the full metric in this second-order approximation. The physical interpretation and meaning of many of the derived relations are discussed. In particular, we can identify the Bondi energy-momentum - given in terms of the Maxwell field - and their evolution. Of particular attractiveness is the observation of an angular momentum conservation law that comes directly from the asymptotic terms in the Bianchi identities. This law contains a flux term that is a confirmation of a classical E&M result but obtained directly from GR.