Ergoregion instability in bosonic stars: scalar mode structure, universality, and weakly nonlinear effects

Abstract

Ultracompact spinning horizonless spacetimes with ergoregions are subject to the ergoregion instability. We systematically investigate the instability of a massless scalar field in a variety of rapidly spinning Proca stars and boson stars using WKB-, frequency-, and time-domain methods. We find universal features in the mode structure: the onset of the instability is signaled by a zero-mode, the mode frequencies and growth rates are related by a simple scaling relation in the small-frequency limit (as found for Kerr-like objects), the mode frequencies approach the orbital frequency of counter-rotating stably trapped null geodesics in the eikonal limit, and for each unstable azimuthal mode only a finite number of overtones and polar modes are exponentially growing. The e-folding times are as short as $\tau \sim 10^{4}M$ (in terms of the spacetime's ADM mass $M$). Interestingly, we find a near universal relationship between the frequencies and growth rates across all bosonic stars and also compared with Kerr-like objects. Furthermore, we show that weakly nonlinear backreaction of the instability induces a shift in growth rates as well as emission of gravitational waves; we find evidence that these effects lead to an amplification of the unstable process. This suggests that strongly nonlinear interactions are important during the gravitational saturation of the instability.

16 pages, 12 figures

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Cited by in corpus (1)

• Nonlinear evolution of the ergoregion instability: Turbulence, bursts of radiation, and black hole formation