Non-aligned Einstein–Maxwell Robinson–Trautman fields of Petrov type D

Abstract

We discuss Petrov type D Einstein–Maxwell (EM) fields in which both double null eigenvectors of the Weyl tensor are non-aligned with the eigenvectors of a non-null electromagnetic field and are assumed to be geodesic, shear-free, diverging and non-twisting. We obtain the general solution of the EM equations under the extra condition that the complex null vectors of the Weyl canonical tetrad are hypersurface orthogonal. The corresponding space–times are all conformally related to a Killing–Yano space and are described by a 5-parameter family of metrics, admitting two commuting Killing vectors and having the C-metric as a possible vacuum limit.