A New Non-Inheriting Homogeneous Solution of the Einstein-Maxwell Equations with Cosmological Term

TL;DR

This paper presents a novel homogeneous solution to the Einstein-Maxwell equations with a cosmological constant, characterized by a specific spacetime topology, symmetry group, and electromagnetic field properties.

Contribution

It introduces a new non-inheriting, homogeneous Einstein-Maxwell solution with a $R imes S^3$ topology and a simply transitive isometry group, expanding the set of known solutions.

Findings

The solution is geodesically complete and globally hyperbolic.

The electromagnetic field is non-null and non-inheriting, invariant under $SU(2)$.

The spacetime is of Petrov type I.

Abstract

We find a new homogeneous solution to the Einstein-Maxwell equations with a cosmological term. The spacetime manifold is $R \times S^3$. The spacetime metric admits a simply transitive isometry group $G = R \times SU(2)$ of isometries and is of Petrov type I. The spacetime is geodesically complete and globally hyperbolic. The electromagnetic field is non-null and non-inheriting: it is only invariant with respect to the $SU(2)$ subgroup and is time-dependent in a stationary reference frame.