Weakly Turbulent Saturation of the Nonlinear Scalar Ergoregion Instability
Phys. Rev. Lett. 136, 171401 – Published 28 April, 2026
DOI: https://doi.org/10.1103/ytqg-v1j8
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 counterrotating stable light ring is filled with a spectrum of higher-order azimuthal modes forming a ringlike 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.
