Maxwell equations in homogeneous spaces with solvable groups of motions

TL;DR

This paper classifies all exact solutions of Maxwell vacuum equations in homogeneous spaces with Bianchi type VII symmetry, providing a complete set of solutions and explicit electromagnetic potentials.

Contribution

It completes the classification of Maxwell vacuum solutions in homogeneous spaces with Bianchi type VII symmetry, including explicit potentials and canonical frames.

Findings

All non-equivalent solutions for Maxwell vacuum equations with Bianchi type VII symmetry are obtained.

Electromagnetic field potentials and canonical frames are explicitly constructed.

The classification fills a gap in understanding electromagnetic fields in these homogeneous spaces.

Abstract

The classification of exact solutions of Maxwell vacuum equations for the case when the electromagnetic fields and metrics of homogeneous spaces are invariant with respect to the motion group G(VII) is completed. All non-equivalent exact solutions of Maxwell vacuum equations for electromagnetic fields and spaces with such symmetry have been obtained. The vectors of the canonical frame of a homogeneous space of type VII according to the Bianchi classification, and the electromagnetic field potentials have been found.