Conformal transformations and weak field limit of scalar-tensor gravity

Abstract

The weak field limit of scalar tensor theories of gravity is discussed in view of conformal transformations. Specifically, we consider how physical quantities, like gravitational potentials derived in the Newtonian approximation for the same scalar-tensor theory, behave in the Jordan and in the Einstein frame. The approach allows to discriminate features that are invariant under conformal transformations and gives contributions in the debate of selecting the true physical frame. As a particular example, the case of f (R) gravity is considered.

Chameleon effect in the Jordan frame of the Brans-Dicke theory

“…However, no matter how trivial the question seems, the debate has not ceased for over the last 53 years [50][51][52][53][54]. In the present section we want to extend the debate to the discussion on the physical implications of the chameleon effect for the BD theory.…”

“…There is an ongoing debate on whether theory (1) or theory (56), has the physical meaning [49][50][51][52][53][54]. In this regard, the chameleon effect has been investigated, exclusively, in the Einstein frame version of the scalar-tensor theory.…”

“…The conformal transformations controversy [49][50][51] is still a subject of debate [52][53][54]. Under a conformal transformation of the metric:…”

Exact scalar-tensor cosmological solutions via Noether symmetry

“…The weak field limit of STT of gravitation was discussed in view of conformal transformations in Stabile et al (2013), and a new reconstruction method of STT based on the use of conformal transformations was proposed. This method allows the derivation of a set of interesting exact cosmological solutions in Brans-Dicke gravity, as well as in other extensions of GR (Vignolo et al 2013).…”

Casimir effect in extended theories of gravity

“…The weak-field limit of such proposals have to be tested against realistic self-gravitating systems. Galactic rotation curves, stellar hydrodynamics and gravitational lensing appear natural candidates as test-bed experiments [17][18][19][20][21][22].…”