Reference frame dependence of the periodically oscillating Coulomb field in the Proca theory

The Proca theory of the real massive vector field admits non-equilibrium solutions, where the asymptotic dynamics of the electric field is dominated by the periodically oscillating Coulomb component. We discuss how such field configurations are seen in different reference frames, where we find an intriguing spatial pattern of the vector field and the electromagnetic field associated with it. Our studies are carried out in the framework of the classical Proca theory.