Black Hole Spectroscopy: from a mathematical problem to an observational reality

This dissertation introduces the reader to the emerging field of "Observational Black Hole Spectroscopy", and the candidate's contributions to the development of the field itself. Black holes quasi-normal oscillations constitute, after a short transient phase, the principal emission process driving the response of a black hole to a perturbation and its return to equilibrium, a process named "ringdown". The candidate's doctoral work was mainly devoted to the analysis of these ringdown signals, with a focus on extracting implications on fundamental physics from gravitational-wave ringdown observations. The technical complications arising in the analysis of black hole vibrations have led the candidate and collaborators to propose a time-domain analysis formalism, which avoid the biases induced by standard frequency-domain analyses. The approach has later been adopted, after internal vetting, by the LIGO-Virgo-KAGRA collaboration to conduct tests of general relativity. By systematically applying such analysis infrastructure to all the ringdown signals detected by the LIGO-Virgo-KAGRA collaboration, we managed to obtain a series of observational results with several fundamental physics implications. In all these analyses, no statistically significant violations of general relativity or the Kerr black hole hypothesis have been detected.