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

TL;DR

This paper derives a general class of Petrov type D Einstein-Maxwell solutions with specific null vector properties, revealing a 5-parameter family of metrics related to known solutions like the C-metric.

Contribution

It provides the first explicit general solution for non-aligned Petrov type D Einstein-Maxwell fields with hypersurface orthogonal null vectors.

Findings

Solutions form a 5-parameter family of metrics.

All solutions are conformally related to a Killing-Yano space.

Includes the C-metric as a vacuum limit.

Abstract

We discuss Petrov type D Einstein-Maxwell 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 Einstein-Maxwell 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.