There are two basic ways that spatially extended magnetic fields are realized in general relativity –

- Static, gravitationally bound flux tubes
- Homogeneous, but anisotropic cosmologies

In our paper Jennie Traschen and I observed that the spacetime metrics associated with these two very different types of solutions are actually very closely related – mapping into one another via the interchange of time and space coordinates. (This is very similar to what is known as the “domain wall/cosmology correspondence” in the context of AdS/CFT.)

We go on to explore various generalizations of the basic Melvin flux tube and magnetic cosmologies, examining how they interpolate at small and large cylindrical radii, or at early and late times, between different vacuum limits.