The Melvin universe in Born-Infeld theory and other theories of nonlinear electrodynamics (Q2724795)

The authors obtain a generalization of the Melvin spacetime as a universe type solution describing a magnetic field permeating the whole universe in gravity minimally coupled to any nonlinear electromagnetic theory, including Born-Infeld theory. The approach relies on a limiting procedure in Einstein-Maxwell theory which transforms the Reissner-Nordström solution into the Melvin solution. For a large set of nonlinear electromagnetic theories, the obtained solution is complete and nonsingular as long as the magnetic field is sub-critical. This solution may help to understand phenomena such as black hole pair creation in gravity coupled to NLE and causality in string theory and NLE. The generalized Melvin solution allows to give examples of gravitational waves travelling in a curved spacetime along the direction in which the Boillat and Einstein lightcones coincide.