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

G. W. Gibbons·C. A. R. Herdeiro
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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.

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G. W. Gibbons, C. A. R. Herdeiro. 2001-01-31. The Melvin Universe in Born-Infeld Theory and other Theories of Non-Linear Electrodynamics. https://doi.org/10.1088/0264-9381%2F18%2F9%2F305

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