Spectral instabilities in the time domain

Quasinormal-mode frequencies characterize black-hole spacetimes and can be measured with gravitational waves, but small perturbations to the gravitational potential can substantially change the spectrum. This seminar studies that spectral instability in a time-domain waveform model. A frequency shift appears only after a delay set by the echo time between the perturbation and the primary potential. In the perturbative limit, the post-echo shift agrees with the usual frequency-domain result; outside that limit, the intermediate-time signal cannot be represented by a constant frequency shift.