Physical Significance of the Black Hole Quasinormal Mode Spectra Instability

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