Instability of a rotating black hole in a limited form of f(R) gravity

We investigate the stability of f(R)-rotating (Kerr) black hole obtained from a limited form of f(R) gravity. In order to avoid the difficulty of handling fourth order linearized equations, we transform this form of f(R) gravity into the scalar-tensor theory by introducing two auxiliary scalars. In this case, the linearized curvature scalar equation leads to a massive scalaron equation. It turns out that the f(R)-rotating black hole is unstable because of the superradiant instability known as the black-hole bomb idea.