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

TL;DR

This paper demonstrates that conformally related 'veiled' versions of General Relativity produce identical observational predictions to the original theory, highlighting the physical equivalence under Weyl rescaling.

Contribution

It shows that conformal transformations in gravity theories do not alter observable predictions, emphasizing the equivalence of different metric representations in General Relativity.

Findings

Conformal transformations preserve observational predictions.

Weyl rescaling interpreted as spacetime-dependent inertial mass.

'Veiled' theories are observationally indistinguishable from standard GR.

Abstract

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.