Exact Solutions of Maxwell Vacuum Equations in Null Homogeneous Petrov Spaces with Non-Solvable Motion Groups

A complete classification is conducted of the exact solutions of Maxwell vacuum equations for invariant electromagnetic fields in null homogeneous Petrov spaces with non-solvable groups of motions G3, acting simply transitively on null hypersurfaces of null homogeneous Petrov spaces. The classification of exact solutions to Maxwell vacuum equations is based on using the representation of components of the contravariant metric tensor and components of the invariant electromagnetic field in terms of the vector fields of a canonical frame. The classification results are presented in a form convenient for further use.