  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.
