Static Spherically Symmetric Solutions in F(R) Gravity

TL;DR

This paper derives a simplified method to find exact static spherically symmetric solutions in F(R) gravity, recovering known solutions and presenting a new non-trivial solution with variable Ricci scalar.

Contribution

It introduces a unified approach to reduce the equations of motion to a single equation, enabling the construction of new exact solutions in F(R) gravity.

Findings

Recovered all known exact solutions.

Derived a new non-trivial solution with non-constant Ricci scalar.

Provided a systematic method for solving F(R) gravity equations.

Abstract

A Lagrangian derivation of the Equation of Motion (EOM) for static spherically symmetric metrics in F(R) modified gravity is presented. For a large class of metrics, our approach permits to reduce the EOM to a single equation and we show how it is possible to construct exact solutions in $F(R)$-gravity. All known exact solutions are recovered. We also exibit a new non trivial solution with non constant Ricci scalar.