A note on the linear stability of black holes in quadratic gravity

Abstract

Black holes in $f(R)$-gravity are known to be unstable, especially the rotating ones. In particular, an instability develops that looks like the classical black hole bomb mechanism: the linearized modified Einstein equations are characterized by an effective mass that acts like a massive scalar perturbation on the Kerr solution in General Relativity, which is known to yield instabilities. In this note, we consider a special class of $f(R)$ gravity that has the property of being scale-invariant. As a prototype, we consider the simplest case $f(R)=R^2$ and show that, in opposition to the general case, static and stationary black holes are stable, at least at the linear level.

arXiv commentLittle changes, version accepted by EPJ Plus

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Cited by in corpus (6)

• Beyond Schwarzschild-de Sitter spacetimes: II. An exact non-Schwarzschild metric in pure $R^2$ gravity and new anomalous properties of $R^2$ spacetimes
• Testing scale-invariant inflation against cosmological data
• Inflation and primordial gravitational waves in scale-invariant quadratic gravity with Higgs
• Beyond Schwarzschild-de Sitter spacetimes: III. A perturbative vacuum with non-constant scalar curvature in $R+R^2$ gravity
• A stationary axisymmetric vacuum solution for pure $R^2$ gravity
• On the stability of scale-invariant black holes