Electromagnetically and gravitationally stealth fields

We construct a generic class of models for complex scalar fields — minimally coupled to gravity and electromagnetism — with the property that their energy-momentum tensor and the electric current vanish for certain massive configurations. These are electromagnetically and gravitationally stealth fields. We shall see that the latter configurations can affect, in addition, the strength of the gravity-matter and electromagnetic-matter couplings of other (non-stealth) modes present in the system, which turn out to be equivalent to the re-scaling the electric charge and the Newton constant (with a stealth-mass depending factor).