Weak Field Approach in f(R)-Gravity

TL;DR

This paper explores the weak field and Newtonian limits of f(R)-Gravity, demonstrating that it recovers General Relativity results in the Solar System, countering claims of its local-scale viability issues.

Contribution

It clarifies the Newtonian limit of f(R)-Gravity and shows that Einstein's theory is a special case, supporting its viability at local scales.

Findings

f(R)-Gravity recovers General Relativity in the weak field limit

Spherically symmetric solutions are consistent with Solar System tests

Counteracts literature claims about the non-viability of f(R)-Gravity at local scales

Abstract

In this communication we discuss the Weak Field Approach, and in particular the Newtonian limit, applied to f(R)-Gravity. Particular emphasis is placed on the spherically symmetric solutions and finally, it is clearly shown that General Relativity results, in the Solar System context, are easily recovered since Einstein theory is a particular case of $f(R)$-Gravity. This is a crucial point against several wrong results in literature stating that these theories are not viable at local scales.