Asymptotically flat vacuum solution for a rotating black hole in a modified gravity theory

Abstract: The theory of f(R)-gravity is one of the theories of modified Einstein gravity. The vacuum solution, on the other hand, of the field equation is the solution for black hole geometry. We establish here an asymptotically flat rotating black hole solution in an f(R)-gravity. This essentially leads to the modified solution to the Kerr black hole. This solution exhibits the change in fundamental properties of the black hole and its geometry. It particularly shows that radii of marginally stable and bound orbits and black hole event horizon increase compared to those in Einstein gravity, depending on the modified gravity parameter. It further argues for faster spinning black holes with spin (Kerr) parameter greater than unity, without any naked singularity. This supports the weak cosmic censorship hypothesis.