Isospectrality breaking beyond General Relativity: classification and observable signatures

Accurately modeling a gravitational-wave ringdown signal, dominated by quasinormal modes, is crucial to test the accuracy of general relativity (GR). Many modified theories of gravity predict the even- and odd-parity ringdown modes have different quasinormal mode frequencies, violating the symmetry (isospectrality) found in GR. In this paper, we use the recently developed modified Teukolsky equations to classify how isospectrailty breaking can occur in effective-field-theory extensions of GR. We find that in a broad range of modifications, isospectrality is lost, leaving possible evidence for parity-violating gravity and the existence of additional scalar, vector, or tensor fields. Additionally, we use numerical relativity simulations to model the signal-to-noise ratio of modified waveforms in next-generation detectors, forecasting the optimal properties of progenitor binaries that could produce a detectable isospectrality-breaking signal.