Stability of the fundamental quasinormal mode in time-domain observations against small perturbations

Black hole spectroscopy with gravitational waves is an important tool to measure the mass and spin of astrophysical black holes test their Kerr nature. Next-generation ground- space-based detectors will observe binary mergers large signal-to-noise ratios perform routinely. It was recently shown that small perturbations due, e.g., environmental effects (the "flea") effective potential governing gravitational-wave generation propagation in exteriors "elephant") can lead arbitrarily changes hole's quasinormal spectrum, including fundamental mode, which expected dominate observed signal. This raises question: program robust against perturbations? We clarify physical behavior time-domain signals under potential, we show amplitude mode prompt ringdown signal are parametrically small. implies extracted from observable stable perturbations. The stability overtones deserves further investigation.