Revised spherically symmetric solutions of $R+\varepsilon/R$ gravity

TL;DR

This paper investigates spherically symmetric solutions in an $f(R)$ gravity model, finding Schwarzschild solutions and modifications that could explain cosmic acceleration without dark energy.

Contribution

It provides exact and perturbed Schwarzschild solutions in $R+rac{ ext{const}}{R}$ gravity, linking local and large-scale gravitational effects.

Findings

Schwarzschild metric is an exact solution in the model.

Perturbed solutions are viable for solar system tests.

Large-scale solutions include a logarithmic term causing repulsive gravity.

Abstract

We study spherically symmetric static empty space solutions in $R+\varepsilon/R$ model of $f(R)$ gravity. We show that the Schwarzschild metric is an exact solution of the resulted field equations and consequently there are general solutions which {are perturbed Schwarzschild metric and viable for solar system. Our results for large scale contains a logarithmic term with a coefficient producing a repulsive gravity force which is in agreement with the positive acceleration of the universe.