  Electromagnetic potentials allow for an alternative description of the
Maxwell field, the electric and magnetic components of which emerge as
gradients of the vector and the scalar potential. We provide a general
relativistic analysis of these potentials, by deriving their wave equations in
an arbitrary Riemannian spacetime containing a generalised imperfect fluid.
Some of the driving agents in the resulting wave formulae are explicitly due to
the curvature of the host spacetime. Focusing on the implications of
non-Euclidean geometry, we look into the linear evolution of the vector
potential in Friedmann universes with nonzero spatial curvature. Our results
reveal a qualitative difference in the evolution of the potential between the
closed and the open Friedmann models, solely triggered by the different spatial
geometry of these spacetimes. We then consider the interaction between
gravitational and electromagnetic radiation and the effects of the former upon
the latter. In so doing, we apply the wave formulae of both potentials to a
Minkowski background and study the Weyl-Maxwell coupling at the second
perturbative level. Our solutions, which apply to low-density interstellar
environments away from massive compact stars, allow for the resonant
amplification of both the electromagnetic potentials by gravitational-wave
distortions.
