Geometry of Gravitation and Electromagnetism

Abstract

An independent derivation is given of equations first derived by Rainich which show how, under certain circumstances, the combined theory of gravitation and electromagnetism of Einstein and Maxwell can be unified and described exclusively in terms of geometry. Some algebraic relations are presented between the Ricci tensor, the electromagnetic field tensor, and their principal null vectors. It is shown that in regions of space-time where the two invariants of the electromagnetic field both vanish, the unified theory cannot apply. Either such regions do not exist in nature or their description in terms of pure geometry has yet to be found. Advantage is taken of the correspondences between tensors and spinors to carry out most of the present calculations in spinor space.