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

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.