Electric/magnetic universe with a cosmological constant

TL;DR

This paper derives a new spacetime solution representing a universe with parallel electric/magnetic fields influenced by a cosmological constant, extending known solutions like the Melvin universe to include $ ext{(A)dS}$ backgrounds.

Contribution

It introduces a novel solution for electric/magnetic universes with a cosmological constant, derived as a limit of the C-metric, and analyzes its properties and relation to existing solutions.

Findings

The solution is equivalent to Astorino's solution under coordinate transformation.

For $ ext{(A)dS}$, the spacetime is asymptotically locally anti-de Sitter.

The solution can be obtained via a double-Wick rotation of a charged AdS black hole.

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.