Rotating black hole solutions for $f(R)$ gravity and Newman Janis Algorithm

TL;DR

This paper demonstrates that certain $f(R)$ gravity theories with constant Ricci scalar can be mapped to Einstein or Einstein-Maxwell gravity with a cosmological constant, and introduces a modified Newman-Janis algorithm to generate rotating solutions.

Contribution

It provides a novel method to obtain rotating black hole solutions in $f(R)$ gravity using a modified Newman-Janis algorithm, expanding solution-generating techniques in modified gravity theories.

Findings

$f(R)$ gravity with constant Ricci scalar is equivalent to Einstein/Einstein-Maxwell gravity with a cosmological constant.

A modified Newman-Janis algorithm is proposed for rotating solutions.

Stationary solutions in Einstein gravity correspond to solutions in dual $f(R)$ gravity.

Abstract

We show that the $f(R)$-gravity theories with constant Ricci scalar in the Jordan/Einstein frame can be described by Einstein or Einstein-Maxwell gravity with a cosmological term and a modified gravitational constant. We also propose a modified Newmann-Janis algorithm to obtain the rotating axisymmetric solutions for the Einstein/Einstein-Maxwell gravity with a cosmological constant. Using the duality between the two gravity theories we show that the stationary or static solutions for the Einstein/Einstein-Maxwell gravity with a cosmological constant will also be the solutions for the dual $f(R)$-gravity with constant Ricci scalar.