Hamilton-Jacobi and Klein-Gordon-Fock equations for a charged test particle in space-time with simply transitive four-parameter groups of motions

TL;DR

This paper classifies electromagnetic fields in spacetimes with four-parameter symmetry groups, providing explicit potentials and extending previous classifications to include all such symmetric cases.

Contribution

It offers a complete classification of electromagnetic potentials in spaces with simply transitive four-parameter motion groups, complementing prior coordinate-based results.

Findings

Explicit metric components of electromagnetic potentials are derived.

The work extends previous classifications to all electromagnetic fields with four-parameter symmetry.

Provides a coordinate-free classification of electromagnetic fields in symmetric spacetimes.

Abstract

Metric components of potentials of admissible electromagnetic fields in spaces with simply transitive four-parameter motion group are found. The components of frame vectors corresponding to the components of the metric tensors found by Petrov are given. The results obtained complement the coordinate-free classification given by Magazev et al. Previously, admissible electromagnetic fields were found for the case when three- and four-parameter groups of motions act on hypersurfaces of spacetime. Thus, non-equivalent sets of potentials for all electromagnetic fields that admit three- and four-parameter groups of motions are known now.