Quasibound states of massive scalar around the Kerr black hole

TL;DR

This paper investigates quasibound states of a massive scalar field around Kerr black holes, revealing conditions for superradiant instability and the formation of gravitational atoms, with implications for ultralight bosons.

Contribution

It provides a detailed analysis of quasibound states and their stability criteria, highlighting the role of potential wells in superradiant phenomena around Kerr black holes.

Findings

Identification of trapping and tiny wells affecting bound states

Ultralight bosons can form hydrogen-like gravitational atoms

Criteria for superradiant instability versus stability

Abstract

In this work, we obtain quasibound states of a massive scalar around the Kerr black hole. A massive scalar propagating around the Kerr black hole induces the far-region potential with either a trapping well or a tiny well, which produces a peak of resonance or a bound state in the far-region. The former represents superradiant instability, while the latter could accommodate superradiant instability via a positive $\omega_I$. If the scalar's energy is really quantized around a tiny well, an ultralight boson could be expressed in terms of a hydrogen-like bound state, leading to a gravitational atom when incorporating superradiant instability. If there are no wells outside the outer horizon, their far-region wave functions represent purely bound state without node. Finally, we discriminate between superradiant instability and stability.