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

TL;DR

This paper explores both weak and strong gravitational fields in the $R+rac{ ext{ extmu}^4}{R}$ gravity model, revealing conditions for strong fields and their relation to Schwarzschild solutions.

Contribution

It introduces a new method for analyzing the weak field limit and demonstrates the existence of strong gravitational fields in vacuum within this modified gravity model.

Findings

Weak field limit derived for $f(R)=R+\mu^4/R$

Existence of strong gravitational fields in vacuum shown

Strong and weak fields relate to perturbed Schwarzschild metric as $\mu \to 0$

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 $\mu\rightarrow 0$, the weak field limit and the strong gravitational field can be regarded as a perturbed Schwarzschild metric.