A note on the linear stability of black holes in quadratic gravity
Dipartimento di Fisica, Università di Trento, Via Sommarive 14, 38123, Povo, TN, Italy
2 Trento Institute for Fundamental Physics and Applications (TIFPA)-INFN, Via Sommarive 14, 38123, Povo, TN, Italy
* e-mail: email@example.com
Accepted: 10 November 2020
Published online: 17 November 2020
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. Finally, the result is generalized to a wider class of f(R) theories.
© The Author(s), 2020