Properties of the magnetic universe with positive cosmological constant

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' ℓ ∝ Λ -1/2 and the magnetic field parameter β, and they are warped products of the form R 1,d-3 ×S 2 , where R 1,d-3 is the (d-2)-dimensional Minkowski spacetime and S 2 is topologically a two-sphere which contains a conical singularity, whose nature depends on the product βℓ. In the limit ℓ → ∞, the S 2 decompactifies and the d-dimensionalMelvin 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.