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A general solution in the Newtonian limit of f(R)- gravity
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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.
Forward citations
Cited by 3 Pith papers
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Differential Obstructions to Curvature-Dependent Conformal Transformations
Curvature-dependent conformal transformations such as g-tilde = F(R[g])g are not local changes of metric variables: their inverse requires solving a differential equation, so no finite-jet metric-only inverse exists g...
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Big-Bang Nucleosynthesis and WIMP Dark Matter Freeze-Out as Probes of Yukawa Cosmology
Using BBN and WIMP relic density, the authors constrain the Yukawa gravity coupling α to about -0.017 to 0.018, with the lithium discrepancy still unexplained.
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Nonstatic Reissner-Nordstr\"om metric in the perturbative $f(R)$ theory: Embedding in the background of the FLRW cosmology, uniqueness of solutions, the TOV equation
The paper claims that charged spherically symmetric sources in perturbative f(R) gravity can radiate gravitational waves through a time-dependent exterior metric.
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