Static Spherically Symmetric Solution of (R +- {\mu}^4/R) Gravity

TL;DR

This paper derives a static spherically symmetric solution in a modified f(R) gravity model, showing minimal deviation from Einstein's gravity and dependence on matter distribution shape.

Contribution

It provides a new solution for (R ± μ^4/R) gravity that reduces to Schwarzschild in the limit μ→0, highlighting differences from scalar-tensor equivalence results.

Findings

The metric closely resembles Schwarzschild when μ→0.

Deviation from Einstein gravity is very small.

Vacuum solutions depend on matter distribution shape.

Abstract

The static spherically symmetric solution for (R +- {\mu}^4/R) model of f(R)gravity is investigated. We obtain the metric for space-time in the solar system that reduces to the Schwarzschild metric, when {\mu} tends to zero. For the obtained metric, the deviation from Einstein gravity is very small. This result is different from the other results have been obtained by equivalence between f(R) gravity and scalar tensor theory. Also it is shown that the vacuum solution in the solar system depends on the shape of matter distribution which differ from the Einstein's gravity.