Electric or magnetic universe with a cosmological constant

Abstract

A spacetime consisting of parallel electric/magnetic fields held together by its own gravity in the presence of a cosmological constant $\Lambda$ is derived as a limit of the de Sitter/anti-de Sitter C-metric. The limiting procedure is similar to the $\Lambda=0$ case where the Melvin universe is derived from the C-metric. Under an appropriate coordinate transformation, we show that this solution is equivalent to the solution obtained by Astorino. Some physical and geometrical properties of the solution are studied, as well as its geodesics. For $\Lambda<0$, the solution is asymptotically locally anti-de Sitter, and can be derived as a double-Wick rotation of a charged anti-de Sitter black hole with a planar horizon.