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 {\it 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).