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arXiv · 2206.14953

Superradiant instability of a massive scalar on the Kerr spacetime

Yun Soo Myung
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Abstract

We investigate the superradiant instability of Kerr black holes under a massive scalar perturbation. We obtain a potential $V_i(r)$ when expanding the scalar potential $V_K(r)$ for large $r$. The Newton potential $V_1(r)$ and the far-region potential $V_2(r)$ are used to explore the superradiant instability, while $V_3(r)$ matches a geodesic potential $V_{gK}(r)$ for a neutral particle moving around the Kerr black hole. Thus, $V_{gK}(r)$ is employed to fix the separation constant. We obtain a condition for a trapping well to possess a quasibound state in the Kerr black holes by analyzing the Newton potential $V_1(r)$and far-region wave functions obtained from $V_2(r)$. The other condition for no trapping well (a tiny well) is found to generate an asymptotic bound state. Finally, we discuss an ultralight boson whose potential has a tiny well located at asymptotic region.

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Yun Soo Myung. 2022-06-30. Superradiant instability of a massive scalar on the Kerr spacetime. https://arxiv.org/abs/2206.14953

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