Null electromagnetic fields in the generalized Einstein–Maxwell field theory

Abstract

In this paper solutions to the source-free generalized Einstein–Maxwell field equations with a null electromagnetic field are investigated. It is argued that the principal null congruence of the null electromagnetic field need not be geodesic, shear-free or a repeated principal null congruence of the gravitational field. However, if the principal null congruence of the null electromagnetic field is geodesic and shear-free, then it is shown that it must be hypersurface orthogonal, expansion-free, and a repeated principal null congruence of the gravitational field. The local form of all such solutions of Petrov type III or N is presented.