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

Abstract

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.