Cylindrically symmetric non-aligned Einstein-Maxwell solutions with rotation and pseudorotation of the types O and N

TL;DR

This paper introduces a new cylindrically symmetric Einstein-Maxwell solution featuring rotation and pseudorotation, with conformal flatness, multiple electromagnetic sources, and the existence of closed timelike lines, expanding understanding of cosmological models.

Contribution

It presents a novel exact solution to Einstein-Maxwell equations with unique symmetry and electromagnetic properties, including rotation, pseudorotation, and conformal flatness.

Findings

Solution admits seven Killing vectors including rotating and pseudorotating ones.

Electromagnetic sources include constant null fields and circularly polarized waves.

The spacetime contains closed timelike non-geodesic lines.

Abstract

A new solution to the Einstein-Maxwell field equations is presented describing a cylindrically symmetric homogeneous cosmology. The solution is conformally flat, it possesses seven Killing vectors of which the timelike one is rotating and one of the spacelike, pseudorotating. Our solution also admits a Kerr-Schild form. It is alternatively produced by different electromagnetic sources some of which represent constant null electromagnetic fields, while the others, a circularly polarized plane electromagnetic wave (seemingly, a unique situation in general relativity). The concrete electromagnetic four-potentials are found from the assumption that they are proportional to the Killing covectors. The general solution is obtained for timelike and null geodesics. Finally, we find that this space-time admits closed timelike non-geodesic lines.