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

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