2020/07/31 by Christian Dioguardi, Massimiliano Rinaldi · 12 citations
Mathematics · Physics and Astronomy · #Advanced Differential Geometry Research #Black Holes and Theoretical Physics #Black hole (networking) #Classical mechanics #Cosmology and Gravitation Theories #Einstein #General relativity #Geometry #Gravitation #Instability #Mathematical physics #Mathematics #Mechanics #Perturbation (astronomy) #Physics #Quadratic equation #Quantum mechanics #gr-qc #hep-th
paper · pdf · doi:10.1140/epjp/s13360-020-00935-2
published in The European Physical Journal Plus 135(11) (Springer Science+Business Media) · Little changes, version accepted by EPJ Plus
openalex publication_date 2020/11/01 · arxiv created 2020/11/10 · arxiv updated 2020/11/12 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
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 <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mi>f</mml:mi> <mml:mrow> <mml:mo>(</mml:mo> <mml:mi>R</mml:mi> <mml:mo>)</mml:mo> </mml:mrow> <mml:mo>=</mml:mo> <mml:msup> <mml:mi>R</mml:mi> <mml:mn>2</mml:mn> </mml:msup> </mml:mrow> </mml:math> 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.