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arXiv · 1907.09118

Superradiant stability of the Kerr black holes

Jia-Hui Huang·Wen-Xiang Chen·Zi-Yang Huang·Zhan-Feng Mai
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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 $\mu\geq \sqrt{2}m\Omega_H$, 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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Jia-Hui Huang, Wen-Xiang Chen, Zi-Yang Huang, Zhan-Feng Mai. 2019-07-22. Superradiant stability of the Kerr black holes. https://doi.org/10.1016/j.physletb.2019.135026

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