Imprints of Changing Mass and Spin on Black Hole Ringdown

TL;DR

This study numerically examines how changes in a black hole's mass and spin due to gravitational radiation reaction influence the ringdown waveform, revealing significant nonlinear effects and their impact on waveform modeling.

Contribution

It demonstrates the nonlinear deviations in quasinormal mode amplitudes and frequencies caused by mass and spin changes, highlighting the importance of nonlinear effects in black hole ringdown analysis.

Findings

Nonlinear distortions can reach up to 50% in mode amplitudes.

Mass and spin changes cause a drift in quasinormal mode frequencies.

Linear models remain effective from the waveform peak onwards.

Abstract

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 $\sim 5\%$, 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 $\sim 50\%$ 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. %These two nonlinear effects together create a large distortion in both the amplitude and phase of the ringdown gravitational waveform. 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 onwards.