Generating new magnetic universe solutions from old

TL;DR

This paper uses solution-generating techniques to create new, non-singular magnetic universe solutions in Einstein-Maxwell theory, including rotating and evolving universes, with detailed electromagnetic field descriptions.

Contribution

It introduces new non-singular magnetic universe solutions derived from seed solutions using Ehlers transformation, expanding the set of known Einstein-Maxwell solutions.

Findings

Three new non-singular magnetic universe metrics generated.

Two solutions describe rotating magnetic universes.

One solution describes an evolving magnetic universe.

Abstract

In this paper we apply the techniques which have been developed over the last few decades for generating nontrivially new solutions of the Einstein-Maxwell equations from seed solutions for simple spacetimes. The simple seed spacetime which we choose is the "magnetic universe" to which we apply the Ehlers transformation. Three interesting non-singular metrics are generated. Two of these may be described as "rotating magnetic universes" and the third as an "evolving magnetic universe." Each is causally complete - in that all timelike and lightlike geodesics do not end in a finite time or affine parameter. We also give the electromagnetic field in each case. For the two rotating stationary cases we give the projection with respect to a stationary observer of the electromagnetic field into electric and magnetic components.