Conformal equivalence in classical gravity: the example of "veiled" General Relativity

In the theory of General Relativity, gravity is described by a metric which couples minimally to the fields representing matter. We consider here its “veiled” versions where the metric is conformally related to the original one and hence is no longer minimally coupled to the matter variables. We show on simple examples that observational predictions are nonetheless exactly the same as in General Relativity, with the interpretation of this “Weyl” rescaling “`a la Dicke”, that is, as a spacetime dependence of the inertial mass of the matter constituents.