A general solution in the Newtonian limit of f(R)- gravity

Abstract

We show that any analytic $f(R)$-gravity model, in the metric approach, presents a weak field limit where the standard Newtonian potential is corrected by a Yukawa-like term. This general result has never been pointed out but often derived for some particular theories. This means that only $f(R)=R$ allows to recover the standard Newton potential while this is not the case for other relativistic theories of gravity. Some considerations on the physical consequences of such a general solution are addressed.

arXiv comment5 pages

References in corpus (39)

• Introduction to Modified Gravity and Gravitational Alternative for Dark Energy
• Is Cosmic Speed-Up Due to New Gravitational Physics?
• Models of f(R) Cosmic Acceleration that Evade Solar-System Tests
• Curvature Quintessence
• Modified f(R) gravity consistent with realistic cosmology: from matter dominated epoch to dark energy universe
• Extended Theories of Gravity and their Cosmological and Astrophysical Applications
• Cosmological viability of f(R)-gravity as an ideal fluid and its compatibility with a matter dominated phase
• 1/R gravity and Scalar-Tensor Gravity
• Unifying inflation with LambdaCDM epoch in modified f(R) gravity consistent with Solar System tests
• Study of the anomalous acceleration of Pioneer 10 and 11
• Indication, from Pioneer 10/11, Galileo, and Ulysses Data, of an Apparent Anomalous, Weak, Long-Range Acceleration
• Curvature quintessence matched with observational data
• Reconciling dark energy models with f(R) theories
• Low surface brightness galaxies rotation curves in the low energy limit of $R^n$ gravity : no need for dark matter?
• Where new gravitational physics comes from: M-theory?
• f(R) Gravity and scalar-tensor theory
• 1/R Curvature Corrections as the Source of the Cosmological Acceleration
• Spherically symmetric solutions of modified field equations in f(R) theories of gravity
• The Power of General Relativity
• Solar System constraints to general f(R) gravity
• The Newtonian Limit of F(R) gravity
• Cosmological dynamics of R^n gravity
• Solar system and equivalence principle constraints on f(R) gravity by chameleon approach
• Dark Energy: the equation of state description versus scalar-tensor or modified gravity
• Palatini form of 1/R gravity
• Accelerated Cosmological Models in Ricci squared Gravity
• Solar System tests DO rule out 1/R gravity
• Higher order gravity theories and scalar tensor theories
• Solar System experiments do not yet veto modified gravity models
• PPN-limit of Fourth Order Gravity inspired by Scalar-Tensor Gravity
• Cosmological Evolution in 1/R-Gravity Theory
• The nearly Newtonian regime in Non-Linear Theories of Gravity
• Modified Friedmann Equations in R${}^{-1}$-Modified Gravity
• Post-Newtonian Parameters from Alternative Theories of Gravity
• f(R) theories of gravity in Palatini approach matched with observations
• Theory of gravitation theories: a no-progress report
• The Cauchy problem of f(R) gravity
• On Higher Order Gravities, Their Analogy to GR, and Dimensional Dependent Version of Duff's Trace Anomaly Relation
• Breakdown of the initial value formulation of scalar-tensor gravity and its physical meaning

Cited by in corpus (45)

• Extended Theories of Gravity
• Testing General Relativity with Low-Frequency, Space-Based Gravitational-Wave Detectors
• Towards Understanding Astrophysical Effects of Nuclear Symmetry Energy
• Linearized f(R) Gravity: Gravitational Radiation & Solar System Tests
• On the 1/c Expansion of f(R) Gravity
• Constraining the range of Yukawa gravity interaction from S2 star orbits
• Weak Field Limit and Gravitational Waves in $f(T,B)$ Teleparallel Gravity
• A new framework for studying spherically symmetric static solutions in f(R) gravity
• Constraining the range of Yukawa gravity interaction from S2 star orbits II: Bounds on graviton mass
• Newtonian, Post Newtonian and Parameterized Post Newtonian limits of f(R, G) gravity
• The mass-radius relation for neutron stars in $f(R)=R+\alpha R^2$ gravity: a comparison between purely metric and torsion formulations
• Probing hybrid modified gravity by stellar motion around Galactic Centre
• Testing Yukawa-like potentials from f(R)-gravity in elliptical galaxies
• Systematic biases on galaxy haloes parameters from Yukawa-like gravitational potentials
• Constraining Extended Gravity Models by S2 star orbits around the Galactic Centre
• Hints of Modified Gravity in Cosmos and in the Lab?
• Sub-millimeter Spatial Oscillations of Newton's Constant: Theoretical Models and Laboratory Tests
• Estimating the Parameters of Extended Gravity Theories with the Schwarzschild Precession of S2 Star
• The most general fourth order theory of Gravity at low energy
• Constraints on Spatially Oscillating Sub-mm Forces from the Stanford Levitated Microsphere Experiment Data
• The Post-Newtonian Limit of f(R)-gravity in the Harmonic Gauge
• Probing the dark matter issue in f(R)-gravity via gravitational lensing
• R^n gravity and the chameleon
• The tetralogy of Birkhoff theorems
• Spherically symmetric solution of $f(R,\mathcal{G})$ gravity at low energy
• Pressure effects in the weak-field limit of f(R) = R + alpha R^2 gravity
• Breaking the EOS-Gravity Degeneracy with Masses and Pulsating Frequencies of Neutron Stars
• Dark Universe Phenomenology from Yukawa Potential?
• Nuclear constraints on non-Newtonian gravity at femtometer scale
• Estimating the parameters of Hybrid Palatini gravity model with the Schwarzschild precession of S2, S38 and S55 stars: case of bulk mass distribution
• Tracking the Local Group Dynamics by Extended Gravity
• Addressing the Hubble tension in Yukawa cosmology?
• Perturbative solutions of the $f(R)$-theory of gravity in a central gravitational field and some applications
• GINGER
• Self-gravitating systems in Extended Gravity
• Apparent Dark Matter Inspired by Einstein Equation of State
• Neutrino oscillation phase dynamically induced by f(R)-gravity
• Hollowgraphy Driven Holography: Black Hole with Vanishing Volume Interior
• Scalar tachyonic instabilities in gravitational backgrounds: Existence and growth rate
• Probing Short Gravity using Temporal Lensing
• Velocity dispersion of dark matter deficient ultra-diffuse galaxies: A case for modified gravity
• Proposed experimental test of Randall-Sundrum Models
• Tests of Classical Gravity with Radio Pulsars
• Nonstatic Reissner-Nordström metric in the perturbative $f(R)$ theory: Embedding in the background of the FLRW cosmology, uniqueness of solutions, the TOV equation
• Non-Newtonian gravity in finite nuclei