Einstein‐Maxwell Equations: Gauge Formulation and Solutions for Radiating Bodies

The subject of the SL(2, c) gauge theory of gravitation is reviewed. A detailed discussion is given on the differential geometry and the fibre bundle structure of such a theory. The coupling of Maxwell's field equations to those of gravitation is also given. The field equations obtained, which are shown to be equivalent to the coupled Einstein‐Maxwell equations, are subsequently solved. The solutions sought after are radiating type ones of the kind of the Kerr metric, but with the mass of the body being variable and is a function of the retarded time. A generalization of the Kerr metric is presented and its energy‐momentum tensor is analyzed in detail. The classification of the field obtained according to the Petrov scheme is also given.