Determine the instability timescale of light-ring compact stars

Determine the timescale of the nonlinear instability that may be driven by the stable light ring generically accompanying the photon sphere in the ultra-compact hybrid and dark-matter-admixed compact-star configurations.

Background

The paper notes that ultra-compact configurations with a light ring generically possess a second, stable light ring. Long-lived modes can accumulate around this stable light ring and potentially trigger a nonlinear instability, but the relevant timescale is not established. Determining this timescale is important for assessing the dynamical viability and observational consequences of the ultra-compact configurations studied in the paper.

References

A spacetime with a light ring generically has a second, stable one, around which the long-lived modes accumulate and may drive a nonlinear instability on a timescale that is not well established ; and the same objects mimic a black hole in the electromagnetic channel as well .

— Ultra-compact twin stars with hybrid equations of state from bosonic dark matter  (2609.03964 - Rather et al., 3 Sep 2026) in Section 3.1, Mass-Radius