New Einstein-Maxwell fields of Levi-Civita's type

TL;DR

This paper applies a conjecture-based method to Levi-Civita vacuum metrics, explicitly deriving new classes of Einstein-Maxwell fields linked to Killing vectors, and analyzes radial geodesic motion in these space-times.

Contribution

It introduces a novel application of the Horsky-Mitskievitch conjecture to Levi-Civita metrics, explicitly finding new Einstein-Maxwell field classes associated with Killing vectors.

Findings

Explicit classes of Einstein-Maxwell fields linked to Killing vectors are derived.

Some of the new classes of solutions are identified as novel contributions.

Radial geodesic motion in these space-times is analyzed and illustrated.

Abstract

The method based on the Horsky-Mitskievitch conjecture is applied to the Levi-Civita vacuum metric. It is shown, that every Killing vector is connected with a particular class of Einstein-Maxwell fields and each of those classes is found explicitly. Some of obtained classes are quite new. Radial geodesic motion in constructed space-times is discussed and graphically illustrated in the Appendix.