The Melvin Universe in Born-Infeld Theory and other Theories of Non-Linear Electrodynamics

TL;DR

This paper constructs a non-singular Melvin Universe solution in gravity coupled to various non-linear electromagnetic theories, including Born-Infeld, analyzing its properties, wave propagation, and dual solutions.

Contribution

It provides the first complete non-singular Melvin Universe solutions in a broad class of non-linear electrodynamics theories, including Born-Infeld, with detailed property analysis.

Findings

Solution is non-singular for sub-critical magnetic fields

Existence of wave solutions along principal null directions

Electric-magnetic duality relates different Melvin universes

Abstract

We derive a Melvin Universe type solution describing a magnetic field permeating the whole Universe in gravity minimally coupled to any non-linear electromagnetic theory, including Born-Infeld Theory. For a large set of non-linear 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 non-standard period along the orbits of the U(1) symmetry to avoid a conical singularity. We show these are consistent with the usual Dirac quantization condition for the magnetic flux. We find exact solutions describing propagation of waves in the `generalized Melvin Universe' along the principal null directions of the electromagnetic field, where the Boillat and Einstein light-cone touch. By electric-magnetic duality we show that similar Melvin electric and dyonic universes can be obtained.