The Melvin universe in Born-Infeld theory and other theories of nonlinear electrodynamics

We derive a Melvin universe-type solution describing a magnetic field perme ating the whole universe in gravity minimally coupled to any nonlinear elec tromagnetic theory, including Born-Infeld theory. For a large set of nonlin ear electrodynamics theories, our solution is complete and non-singular; as long as the magnetic field is sub-critical. We examine some properties of the solution; in particular, there is a shift of the symmetry axis and a no nstandard period along the orbits of the U(1) symmetry to avoid a conical s ingularity. We show these are consistent with the usual Dirac quantization condition for the magnetic flux. We find exact solutions describing propaga tion of waves in the 'generalized Melvin universe' along the principal null directions of the electromagnetic field, where the Boillat and Einstein li ghtcone touch. By electric-magnetic duality we show that similar Melvin ele ctric and dyonic universes can be obtained.