A GENERAL SOLUTION IN THE NEWTONIAN LIMIT OF f(R)-GRAVITY

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.