The Parameterised Post-Newtonian Limit of Fourth-Order Theories of Gravity

Abstract

We determine the full post-Newtonian limit of theories of gravity that extend general relativity by replacing the Ricci scalar, R, in the generating Lagrangian by some analytic function, f(R). We restrict ourselves to theories that admit Minkowski space as a suitable background, and perform a perturbative expansion in the manner prescribed by the parameterised post-Newtonian formalism. Extra potentials are found to be present that are not accounted for in the usual treatment, and a discussion is provided on how they may be used to observationally distinguished these theories from general relativity at the post-Newtonian level.

arXiv comment12 pages

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Cited by in corpus (49)

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• Constraints on Modified Gravity Models from White Dwarfs
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• On the absence of the usual weak-field limit, and the impossibility of embedding some known solutions for isolated masses in cosmologies with f(R) dark energy
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• Cosmological dynamics of fourth order gravity: A compact view
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• Spherical Symmetric Solution in f(R) Model Around Charged Black Hole
• Post-Newtonian parameter $\gamma$ for multiscalar-tensor gravity with a general potential
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• Cyclic cosmology in modified gravity
• Higher Powers in Gravitation
• Rotation Curves of Galaxies by Fourth Order Gravity
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• Weak Gravitational Lensing in Fourth Order Gravity
• Light bending in $F\left[g(\square )R\right]$ extended gravity theories
• Post-Newtonian $\gamma$-like parameters and the gravitational slip in scalar-tensor and $f(R)$ theories
• Distinguishing f(R) theories from general relativity by gravitational lensing effect
• On the stability of spherically symmetric spacetimes in metric f(R) gravity
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• Will-Nordtvedt PPN formalism applied to renormalization group extensions of general relativity
• Relativistic stars in Starobinsky gravity with the matched asymptotic expansions method
• Gravito-magnetic gyroscope precession in Palatini f(R) gravity
• Second-order weak lensing from modified gravity
• Self-gravitating systems in Extended Gravity
• The momentum constraint equation in Parameterised Post-Newtonian Cosmology
• Numerical Analysis of Galactic Rotation Curves
• Simple cosmological model with inflation and late times acceleration
• Scalar wave scattering from Schwarzschild black holes in modified gravity
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• Constraints on a fifth force from the stellar orbits around the central supermassive black hole of the Milky Way
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• Post-Newtonian N-Body Dynamics in Extended Theories of Gravity
• Outperforming classical estimation of Post-Newtonian parameters of Earth's gravitational field using quantum metrology
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