Modified Kerr-Schild Method applied to Gravity f(R)

TL;DR

This paper introduces a modified Kerr-Schild method that maps solutions from General Relativity to Ricci-based Gravity theories, enabling the generation of new solutions in f(R) gravity from known GR solutions.

Contribution

It presents a novel adaptation of the Kerr-Schild method that facilitates solution generation in f(R) gravity by leveraging mappings from GR solutions.

Findings

Successfully maps GR solutions to f(R) gravity configurations.

Enables perturbation of GR metrics within Ricci-based Gravity frameworks.

Provides a systematic approach for deriving solutions in modified gravity theories.

Abstract

We propose an adaptation of the Kerr-Schild method by implementing the correspondence relations (mapping) between Ricci-based Gravity (RBG) and General Relativity (GR). Basically, we generate GR known solutions from a canonical metric with a well-defined form and then obtain the configuration of this solution for the Gravity f(R). The new method allows us to perturb the metric associated with GR with a null geodetic vector, but instead of taking us to a new solution described by Einstein's gravitational sector, it allows us to configure this solution in an RBG.