Maxwell's equations in homogeneous spaces for admissible electromagnetic fields

TL;DR

This paper solves Maxwell's equations in homogeneous spaces for special electromagnetic fields that respect the space's symmetries, providing solutions dependent on arbitrary functions useful for gravity theories.

Contribution

It introduces a method to integrate Maxwell's equations in homogeneous spaces for admissible fields using symmetry-based frames, leading to solutions in quadratures.

Findings

Solutions depend on six arbitrary time functions.

Method applies to integrating field equations in gravity theories.

Provides explicit systems of differential equations for admissible fields.

Abstract

Maxwell's vacuum equations are integrated for admissible electromagnetic fields in homogeneous spaces. Admissible electromagnetic fields are those for which the space group generates an algebra of symmetry operators ( integrals of motion ) that is isomorphic to the algebra of group operators. Two frames associated with the group of motions are used to obtain systems of ordinary differential equations to which Maxwell's equations reduce. The solutions are obtained in quadratures. The potentials of the admissible electromagnetic fields and the metrics of the spaces contained in the obtained solutions depend on six arbitrary time functions, so it is possible to use them to integrate field equations in the theory of gravity.