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

Capozziello, S.; Stabile, A.; Troisi, A.

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

Authors

Capozziello, S.

Stabile, A.

Troisi, A.

Description

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.
5 pages