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.

11 pages, preliminary version

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Cited by in corpus (21)

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• Invariant quantities in the scalar-tensor theories of gravitation
• Selected topics in scalar-tensor theories and beyond
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• Numerical solutions of the modified Lane-Emden equation in f(R)-gravity
• Modified gravity revealed along geodesic tracks
• Astrophysical constraints on extended gravity models
• Casimir effect in quadratic theories of gravity
• Invariant slow-roll parameters in scalar-tensor theories
• Casimir effect in Post-Newtonian Gravity with Lorentz-violation
• Jordan frame no-hair for spherical scalar-tensor black holes
• Casimir effect in Extended Theories of Gravity
• Exact Scalar-Tensor Cosmological Models
• Generalized $R^p$-attractor Cosmology in the Jordan and Einstein Frames: New Type of Attractors and Revisiting Standard Jordan Frame $R^p$ Inflation
• Exact Scalar-Tensor Cosmological Solutions via Noether Symmetry
• Linearized modified gravity theories and gravitational waves physics in the GBD theory
• The Chameleon Effect in the Jordan Frame of the Brans--Dicke Theory
• Self-gravitating systems in Extended Gravity
• Shadows in conformally related gravity theories
• An innovative black hole solution and thermodynamic properties in higher-order curvature gravity with a scalar field
• Precession shift in curvature based Extended Theories of Gravity and Quintessence fields