By means of Debye potentials it is possible to get all solutions of source-free Maxwell equations in vacuum from a single scalar equation. Sufficient conditions for the existence of Debye potentials in a given four-dimensional Riemannian space have been found. Some examples of metrics are given, including plane gravitational waves, metrics with spherical symmetry, and cosmological models. The method is generalized to Maxwell fields with sources and Maxwell fields in dielectric media.
No takes yet. Share an insight, caveat, or question.
Hans Stephani (1974) studied this question.
Synapse has enriched one closely related paper. Consider it for comparative context: