The Newtonian Limit of F(R) gravity

Abstract

A general analytic procedure is developed to deal with the Newtonian limit of $f(R)$ gravity. A discussion comparing the Newtonian and the post-Newtonian limit of these models is proposed in order to point out the differences between the two approaches. We calculate the post-Newtonian parameters of such theories without any redefinition of the degrees of freedom, in particular, without adopting some scalar fields and without any change from Jordan to Einstein frame. Considering the Taylor expansion of a generic $f(R)$ theory, it is possible to obtain general solutions in term of the metric coefficients up to the third order of approximation. In particular, the solution relative to the $g_{tt}$ component gives a gravitational potential always corrected with respect to the Newtonian one of the linear theory $f(R)=R$. Furthermore, we show that the Birkhoff theorem is not a general result for $f(R)$-gravity since time-dependent evolution for spherically symmetric solutions can be achieved depending on the order of perturbations. Finally, we discuss the post-Minkowskian limit and the emergence of massive gravitational wave solutions.

16 pages

References in corpus (13)

• Wilkinson Microwave Anisotropy Probe (WMAP) Three Year Results: Implications for Cosmology
• Extra force in $f(R)$ modified theories of gravity
• Modified f(R) gravity consistent with realistic cosmology: from matter dominated epoch to dark energy universe
• Cosmological viability of f(R)-gravity as an ideal fluid and its compatibility with a matter dominated phase
• Low surface brightness galaxies rotation curves in the low energy limit of $R^n$ gravity : no need for dark matter?
• Spherically symmetric solutions of modified field equations in f(R) theories of gravity
• Spherically symmetric solutions in f(R)-gravity via Noether Symmetry Approach
• Dark energy and dark matter as curvature effects
• Dark Energy: the equation of state description versus scalar-tensor or modified gravity
• Solar System tests DO rule out 1/R gravity
• Fourth order gravity: equations, history, and applications to cosmology
• The behavior of $f(R)$ gravity in the solar system, galaxies and clusters
• Post-Newtonian expansion for Gauss-Bonnet Gravity

Cited by in corpus (99)

• Unified cosmic history in modified gravity: from F(R) theory to Lorentz non-invariant models
• f(R,T) gravity
• Class of viable modified $f(R)$ gravities describing inflation and the onset of accelerated expansion
• f(R,L_m) gravity
• Wormhole geometries in f(R) modified theories of gravity
• Modified f(R) gravity unifying R^m inflation with \LambdaCDM epoch
• Hydrostatic equilibrium and stellar structure in f(R)-gravity
• Modified gravity with arbitrary coupling between matter and geometry
• Good and bad tetrads in f(T) gravity
• The future evolution and finite-time singularities in $F(R)$-gravity unifying the inflation and cosmic acceleration
• Spherical symmetry in $f(R)$-gravity
• The evolution of density perturbations in f(R) gravity
• The matter Lagrangian and the energy-momentum tensor in modified gravity with non-minimal coupling between matter and geometry
• Thin accretion disks in f(R) modified gravity models
• Do f(R) theories matter?
• On the non-minimal gravitational coupling to matter
• Charged spherically symmetric black holes in $f(R)$ gravity and their stability analysis
• Dark energy, inflation and dark matter from modified F(R) gravity
• Finite-time Cosmological Singularities and the Possible Fate of the Universe
• On the 1/c Expansion of f(R) Gravity
• Delicate f(R) gravity models with disappearing cosmological constant and observational constraints on the model parameters
• The Cauchy problem of f(R) gravity
• $f(R)$ gravity constrained by PPN parameters and stochastic background of gravitational waves
• A new parametrization of Hubble parameter in $f(Q)$ gravity
• Constraining some Horndeski gravity theories
• Non-Local Gravity Cosmology: an Overview
• Probing Models of Extended Gravity using Gravity Probe B and LARES experiments
• Neutron stars in $f(\mathtt{R},{\mathtt{L}}_{\mathtt{m}})$ gravity with realistic equations of state: joint-constrains with GW170817, massive pulsars, and the PSR J0030+0451 mass-radius from $NICER$ data
• The Parameterised Post-Newtonian Limit of Fourth-Order Theories of Gravity
• A general solution in the Newtonian limit of f(R)- gravity
• Thermodynamic topology of black Holes in f(R) gravity
• Perturbation of the metric around a spherical body from a nonminimal coupling between matter and curvature
• Hints of Modified Gravity in Cosmos and in the Lab?
• A Panorama of Viable $F(R)$ Gravity Dark Energy Models
• The Newtonian limit of metric gravity theories with quadratic Lagrangians
• Standard Cosmological Evolution in a Wide Range of f(R) Models
• Perihelion precession for modified Newtonian gravity
• Post-Newtonian parameter $\gamma$ for multiscalar-tensor gravity with a general potential
• 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
• Thermodynamic topology of topological black hole in $F(R)$-ModMax gravity's rainbow
• Constraints on Yukawa gravity parameters from observations of bright stars
• Magnetized discs and photon rings around Yukawa-like black holes
• Constraining the cosmological model of modified $f(Q)$ gravity: Phantom dark energy and observational insights
• $R^2$ Inflation Revisited and Dark Energy Corrections
• Spherical collapse model and cluster number counts in power law $f(T)$ gravity
• Bouncing cosmologies and stability analysis in symmetric teleparallel $f(Q)$ gravity
• Cosmological acceleration
• Running of the Spectral Index and Inflationary Dynamics of $F(R)$ Gravity
• Modified theory of gravity and the history of cosmic evolution
• Implications of non-analytical f(R) gravity at Solar-System scales
• Stability analysis of f(Q) gravity models using dynamical systems
• On the equivalence between the effective cosmology and excursion set treatments of environment
• Analytic Electrically Charged Black Holes in $F(R)$-ModMax Theory
• Running coupling in electroweak interactions of leptons from f(R)-gravity with torsion
• f(T) cosmology against the cosmographic method: A new study using mock and observational data
• Gravitational collapse in non-minimally coupled gravity: finite density singularities and the breaking of the no-hair theorem
• Constraints on Power Law and Exponential models in $f(Q)$ Gravity
• Topological phantom AdS black holes in $F(R)$ gravity
• A Study of Black Holes in $F(R)-$ModMax Gravity: Gravitational Lensing and Constraints from EHT Observations
• Dynamical reconstruction of the $\Lambda$CDM model in the scalar-tensor representation of $f\left(Q,T\right)$ gravity
• Astrophysical structures from primordial quantum black holes
• Two-dimensional Lifshitz-like AdS black holes in $F(R)$ gravity
• Modeling and Analyzing Stability of Hybrid Stars within $f(Q)$ Gravity
• Classical and quantum $f(R)$ cosmology: The big rip, the little rip and the little sibling of the big rip
• Addressing the Hubble tension in Yukawa cosmology?
• Master field equations for spherically symmetric gravitational fields beyond general relativity
• Gravitational wave radiation from periodic orbits and quasi-periodic oscillations in Einstein non-linear Maxwell-Yukawa black hole
• Finslerian extension of an anisotropic strange star in the domain of modified gravity
• Graviton mass due to dark energy as a superconducting medium: theoretical and phenomenological aspects
• On Friedmann-Lema\^ıtre-Robertson-Walker cosmologies in non-standard gravity
• Dynamics of dwarf galaxies in $f(R)$ gravity
• New one-parametric extension of the Starobinsky inflationary model
• Three-dimensional accelerating AdS black holes in $F(R)$ gravity
• Self-gravitating systems in Extended Gravity
• Strong gravitational lensing by black hole in F(R) Euler Heisenberg Gravity's Rainbow
• The coincidence problem in $f(R)$ gravity models
• Probing the nature of Einstein nonlinear Maxwell Yukawa black hole through gravitational wave forms from periodic orbits and quasiperiodic oscillations
• Numerical Analysis of Galactic Rotation Curves
• Moduli stabilization with bulk scalar in nested doubly warped braneworld model
• Cosmological dynamics of interacting dark energy and dark matter in $f(Q)$ gravity
• Mimetic-$f(Q)$ gravity: cosmic reconstruction and energy conditions
• Study of Anisotropic Polytropes in $f(\mathcal{R},\mathrm{T})$ Theory
• Cosmological Models in Modified f(R) Gravity Theories
• The shadow of black holes in $F(R)$-ModMax theory with cosmic strings
• Asymptotically Schwarzschild solutions in $f(R)$ extension of general relativity
• Constraints on a fifth force from the stellar orbits around the central supermassive black hole of the Milky Way
• Galactic dynamics in the presence of scalaron: A perspective from $\mathbf{f}(\mathbf{R})$ gravity
• Two body dynamics in a quadratic modification of general relativity
• Weak Field Limit of the Nonminimally Coupled Weyl Connection Gravity
• Gravitational Waves beyond the Linear Approximation and Gravitational Wave Reflection
• Parameterized Post-Newtonian Analysis of Quadratic Gravity and Solar System Constraints
• Thermodynamics and optical aspects of ModMax black holes in higher order curvature gravity with quintessence dark energy
• Thermodynamics, Phase Transitions, and Geodesic Structure of F(R)-Phantom Banados-Teitelboim-Zanelli (BTZ) Black Holes
• Accelerating electrically charged ModMax black hole solutions in $F(R)$ gravity
• The Equivalence and/or the Effacing principle in $f\left(R\right)$ theories of gravity
• Observational constraints on a modified-gravity model with an exponential function of the curvature using the expansion history, the RSD, and the Pantheon+SH0ES data
• Metric tensor at second perturbation order for spherically symmetric space-times
• Constraining Post-Newtonian f(R) Gravity in the Solar System