Linear stability of nonbidiagonal black holes in massive gravity

Abstract

We consider generic linear perturbations of a nonbidiagonal class of static black-hole solutions in massive (bi)gravity. We show that the quasinormal spectrum of these solutions coincides with that of a Schwarzschild black hole in general relativity, thus proving that these solutions are mode stable. This is in contrast to the case of bidiagonal black-hole solutions which are affected by a radial instability. On the other hand, the full set of perturbation equations is generically richer than that of a Schwarzschild black hole in general relativity, and this affects the linear response of the black hole to external perturbations. Finally, we argue that the generalization of these solutions to the spinning case does not suffer from the superradiant instability, despite the fact that the theory describes a massive graviton.

13 pages, 2 figures; v2: References added; v3: matches published version; v4: acknowledgement added

References in corpus (8)

• Resummation of Massive Gravity
• Testing General Relativity with Present and Future Astrophysical Observations
• Instability of the massive Klein-Gordon field on the Kerr spacetime
• A class of charged black hole solutions in massive (bi)gravity
• Black holes in massive gravity
• Rotating black holes in massive gravity
• On stars, galaxies and black holes in massive bigravity
• Rotating (A)dS black holes in bigravity

Cited by in corpus (18)

• Black-hole Spectroscopy by Making Full Use of Gravitational-Wave Modeling
• Relativistic stars in bigravity theory
• Quasinormal modes of weakly charged Einstein-Maxwell-dilaton black holes
• Higher dimensional nonlinear massive gravity
• Higher dimensional massive bigravity
• Kerr-(Anti-)de Sitter Black Holes: Perturbations and quasi-normal modes in the slow rotation limit
• Instability and no-hair paradigm in d-dimensional charged-AdS black holes
• Black holes and stars in the minimal theory of massive gravity
• Classification and asymptotic structure of black holes in bimetric theory
• Asymptotically flat hairy black holes in massive bigravity
• Identifying modified theories of gravity using binary black-hole ringdowns
• Black Holes in Multi-Metric Gravity
• Vainshtein mechanism in massive gravity nonlinear sigma models
• Waveforms in massive gravity and neutralization of giant black hole ringings
• Overdamped quasibound states inside a Schwarzschild black hole
• Black Holes in Multi-Metric Gravity II: Hairy Solutions and Linear Stability of the Non- and Partially Proportional Branches
• Fundamental fields around compact objects: Massive spin-2 fields, Superradiant instabilities and Stars with dark matter cores
• Dipolar perturbations of nonbidiagonal black holes in bigravity