When does black hole ringdown become a sum of linear quasinormal modes?
In plain words
Fits that include higher overtones often start near the peak of the signal, but near the peak nonlinear effects may mimic overtones. Where linear ringing begins determines which modes can be claimed as detected.
Precise statement
In numerical-relativity waveforms and in data, determine the earliest time $t_0$ after the strain peak at which $h(t)$ is described within numerical error by a finite sum of linear Kerr quasinormal modes with constant amplitudes, and whether overtones fitted before $t_0$ are physical or absorb nonlinear and transient content. An answer is a quantitative criterion for $t_0$, in units of $G M_f/c^{3}$, as a function of mass ratio and spins, validated on simulations.
What would settle it
A systematic comparison of second-order perturbation theory and numerical relativity that fixes $t_0$ and the physical overtone content.
Status in the literature
Unverified note
The GW150914 overtone claim (2019) was disputed (2022-2024); in GW250114 the overtone amplitude departs from the expected decay before about $6 G M_f/c^3$ after the peak (2025).