Superradiant stability of the Kerr black holes

Abstract

We study the superradiant stability of the system of a Kerr black hole and a massive scalar perturbation. It was proved previously that this system is superradiantly stable when $\mu \ge \sqrt{2}m{\Omega }_H$, where $\mu$ is the proper mass of the scalar, $m$ is the azimuthal number of the scalar mode, and ${\Omega }_H$ is the angular velocity of the Kerr black hole horizon. Our study is a complementary work of this result. We analytically prove that in the complementary parameter region $\mu <\sqrt{2}m{\Omega }_H$, when the parameters of scalar perturbation and Kerr black hole satisfy two simple inequalities, $\omega <\frac{\mu }{\sqrt{2}}$,~ $\frac{r_{-}}{r_{+}}<0.802$, the system is also superradiantly stable.

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• Extremal rotating black holes, scalar perturbation and superradiant stability
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• Massive Scalar Perturbation of Extremal Rotating Braneworld Black hole: Superradiant Stability Analysis
• Superradiant stability of five and six-dimensional extremal Reissner-Nordstrom black holes
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• No black hole bomb for D-dimensional extremal Reissner-Nordstrom black holes under charged massive scalar perturbation
• Revisiting superradiant stability of Kerr-Newman black holes under a charged massive scalar
• Does Gravity Render Probability Quasilocal?
• On the five-dimensional non-extremal Reissner-Nordström black hole: Retractions and scalar quasibound states
• Smoking Gun Signatures of Quasilocal Probability in Black Hole Ringdowns