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arXiv · 2510.07467

Weakly turbulent saturation of the nonlinear scalar ergoregion instability

Nils Siemonsen
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Abstract

We perform time-domain evolutions of the ergoregion instability on a horizonless spinning ultracompact spacetime in scalar theories with potential-type and derivative self-interactions mimicking the nonlinear structure of the Einstein equations. We find that the instability saturates by triggering a weakly turbulent direct cascade, which transfers energy from the most unstable and large-scale modes to small scales. The cascade's nonlinear timescales of each mode are orders of magnitude shorter than the corresponding linear e-folding times. Through this mechanism, the counter-rotating stable light ring is filled with a spectrum of higher-order azimuthal modes forming a ring-like shape. Thereby we demonstrate that turbulent processes are likely also important during the fully gravitational saturation of the instability, leaving imprints in the gravitational wave emission.

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Nils Siemonsen. 2025-10-08. Weakly turbulent saturation of the nonlinear scalar ergoregion instability. https://doi.org/10.1103/ytqg-v1j8

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