Optimal strategies for black hole spectroscopy*

Gravitational waves emitted during the final stages of a binary black hole merger, known as the ringdown phase, can be modeled using a combination of quasinormal modes with complex frequencies. Black hole spectroscopy is the art of extracting these frequencies and using them as evidence for the existence of black holes, test the no-hair theorem, and test general relativity. While black hole spectroscopy is a promising and powerful tool, it comes with a number of caveats. When modeling the ringdown waveform, adding too many overtones to the model risks overfitting the waveform near the merger phase, while nonlinear quasinormal modes have to be included for better accuracy. In addition, the quasinormal-mode frequencies are spectrally unstable. Failure to appreciate these subtleties might lead to false-positives in overtone detection and biased results in no-hair theorem tests.