On the Newtonian limit of metric f(R) gravity

The quasi-Newtonian limit for arbitrary gravitational theories of the f ( R ) class is considered. It is shown that only a subclass of these theories have such a limit. The approximate field equation and equations of motion are calculated and discussed. Moreover, the general solutions of the approximate field equation is investigated where especially solutions for point particles are focused. We found that the approximate field equation is in general of fourth-order with a source term which depends not only on the mass density but also on its Laplaceian.