Electromagnetic Sources in General Relativity Theory

Abstract

The simplest, most direct method of unifying Maxwell's theory of electromagnetism and Einstein's theory of gravitation was formulated by Rainich in 1925. That theory applies only to charge-free space. However, in regions of space in which the electromagnetic field invariant corresponding to E\ifmmode\cdot\else\textperiodcentered\fi{}B vanishes, the two sets of Maxwell's equations are independent for Rainich's unified theory. The Rainich theory may be modified to allow for nonvanishing charge and current density in such regions. The electromagnetic sources and fields obey Maxwell-Lorentz theory and the electromagnetic matter-energy obeys the laws of Einstein's general relativity theory. The necessary and sufficient conditions which one must impose on the metric tensor and its derivatives in order to assure the existence of a unique antisymmetric tensor obeying the Maxwell-Lorentz laws in the presence of charges and currents have been derived.