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.

14 pages, no figure, title changed slightly, version to appear in PRD

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• Instability of the massive Klein-Gordon field on the Kerr spacetime
• Kerr Black Holes are Not Unique to General Relativity
• Perturbed Kerr Black Holes can probe deviations from General Relativity
• Stability of f(R) black holes
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