Electromagnetic Solutions of the Field Equations of General Relativity

Abstract

An investigation of the electromagnetic field in general relativity has been undertaken. This study was partially motivated by the recent interest in the intense quasistellar sources and gravitational collapse and relativistic models for such phenomena. Metrics and fields as functions of two or three independent variables are considered. The equations for the case of two independent variables are presented in a simple form, and certain special solutions of these equations are derived, which may have some bearing on gravitational collapse. The major result of this paper may be stated as follows. Suppose given a set of metric coefficients $g_{\mathrm{ik}}$ which are functions of no more than three independent variables and which satisfy the vacuum field equations. We also suppose it possible to express this metric in diagonal form. Then, from this metric, one can find another metric, plus nonzero electromagnetic field, which satisfy the field equations with electromagnetic sources plus Maxwell's equations.