Strong and weak gravitational field in $R+{\mu }^4/R$ gravity

Abstract

We introduce a new approach for investigating the weak field limit of vacuum field equations in $f(R)$ gravity and we find the weak field limit of $f(R)=R+{\mu }^4/R$ gravity. Furthermore, we study the strong gravity regime in $R+{\mu }^4/R$ model of $f(R)$ gravity. We show the existence of strong gravitational field in vacuum for such model. We find out in the limit $\mu \to 0$, the weak field limit and the strong gravitational field can be regarded as a perturbed Schwarzschild metric.

7 pages, 3 figures, to be appear in APSS