Robust approach to f(R) gravity

TL;DR

This paper proposes a direct metric f(R) gravity approach using Ricci scalar as an extra degree of freedom, avoiding scalar-field potential issues, and applies it to static, spherically symmetric spacetimes to address relativistic object existence.

Contribution

It introduces a novel method for f(R) gravity analysis that bypasses scalar-tensor mapping, simplifying the study of relativistic objects in these theories.

Findings

Demonstrates the effectiveness of the Ricci scalar approach in static, spherically symmetric spacetimes.

Addresses the controversy regarding the existence of extended relativistic objects in certain f(R) models.

Abstract

We consider metric f(R) theories of gravity without mapping them to their scalar-tensor counterpart, but using the Ricci scalar itself as an "extra" degree of freedom. This approach avoids then the introduction of a scalar-field potential that might be ill defined (not single valued). In order to explicitly show the usefulness of this method, we focus on static and spherically symmetric spacetimes and deal with the recent controversy about the existence of extended relativistic objects in certain class of f(R) models.