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, weconsider 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.

A note on the linear stability of black holes in quadratic gravity / Dioguardi, Christian; Rinaldi, Massimiliano. - In: THE EUROPEAN PHYSICAL JOURNAL PLUS. - ISSN 2190-5444. - 135:(2020), pp. 920.1-920.9. [10.1140/epjp/s13360-020-00935-2]

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

Rinaldi, Massimiliano
2020-01-01

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, weconsider 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.
2020
Dioguardi, Christian; Rinaldi, Massimiliano
A note on the linear stability of black holes in quadratic gravity / Dioguardi, Christian; Rinaldi, Massimiliano. - In: THE EUROPEAN PHYSICAL JOURNAL PLUS. - ISSN 2190-5444. - 135:(2020), pp. 920.1-920.9. [10.1140/epjp/s13360-020-00935-2]
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11572/280530
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