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arXiv · 1606.02306

The superradiant instability regime of the spinning Kerr black hole

Shahar Hod
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Abstract

Spinning Kerr black holes are known to be superradiantly unstable to massive scalar perturbations. We here prove that the instability regime of the composed Kerr-black-hole-massive-scalar-field system is bounded from above by the dimensionless inequality $Mμ< m \cdot \sqrt{{{2(1+γ) (1-\sqrt{1-γ^2}) - γ^2} \over {4γ^2}}}$, where $\{μ,m\}$ are respectively the proper mass and azimuthal harmonic index of the scalar field and $γ\equiv r_-/r_+$ is the dimensionless ratio between the horizon radii of the black hole. It is further shown that this {\it analytically} derived upper bound on the superradiant instability regime of the spinning Kerr black hole agrees with recent {\it numerical} computations of the instability resonance spectrum.

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Shahar Hod. 2016-06-07. The superradiant instability regime of the spinning Kerr black hole. https://doi.org/10.1016/j.physletb.2016.05.012

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