Physical significance of the black hole quasinormal mode spectra instability

It has been shown, via specific examples and a pseudospectrum analysis, that the black hole quasinormal spectra are unstable. The implication of such a result for gravitational-wave physics and of our understanding of black holes is, still, unclear. The purpose of this work is twofold: (i) we show that some of the setups leading to instabilities are unphysical and triggered by exotic matter or extreme spacetimes; (ii) nevertheless, we also show simple examples of compelling physical scenarios leading to spectral instabilities. Our results highlight the importance of understanding the overtone content of time-domain waveforms, and their detectability.