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)=R2 and show that, in opposition to the general case, static and stationary black holes are stable, at least at the linear level.
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