Properties of the magnetic Universe with positive cosmological constant

Abstract

The properties of the Melvin-type spacetime with a positive cosmological constant Λ in d-dimensional Einstein–Maxwell gravity is studied. The solution is parametrised in terms of the ‘de Sitter radius’ and the magnetic field parameter β, and they are warped products of the form , where is the -dimensional Minkowski spacetime and S2 is topologically a two-sphere which contains a conical singularity, whose nature depends on the product . In the limit , the S2 decompactifies and the d-dimensional Melvin Universe is recovered. The Freund–Rubin-type flux compactification model is shown to be another particular limit of this solution. We also calculate the flux and geodesics in this spacetime.