Imprints of changing mass and spin on black hole ringdown

We numerically investigate the imprints of gravitational radiation-reaction driven changes to a black hole's mass and spin on the corresponding ringdown waveform. We do so by comparing the dynamics of a perturbed black hole evolved with the full (nonlinear) versus linearized Einstein equations. As expected, we find that the quasinormal mode amplitudes extracted from nonlinear evolution deviate from their linear counterparts at third order in initial perturbation amplitude. For perturbations leading to a change in the black hole mass and spin of $\ensuremath{\sim}5%$, which is reasonable for a remnant formed in an astrophysical merger, we find that nonlinear distortions to the complex amplitudes of some quasinormal modes can be as large as $\ensuremath{\sim}50%$ at the peak of the waveform. Furthermore, the change in the mass and spin results in a drift in the quasinormal mode frequencies, which for large amplitude perturbations causes the nonlinear waveform to rapidly dephase with respect to its linear counterpart. Surprisingly, despite these nonlinear effects creating significant deviations in the nonlinear waveform, we show that a linear quasinormal mode model still performs quite well from close to the peak amplitude onward. Comparing the quality of quasinormal mode fits for the linear and nonlinear waveforms, we show that the main obstruction to measuring high-$n$ overtones is the transient part of the waveform, already present at the linear level.