In the presence of external perturbations, astrophysical black holes (BHs) relax toward
a Kerr spacetime, as a consequence of the final state conjecture. During the relaxation
process (ringdown), BHs emit a spectrum given by a superposition of damped
sinusoids whose parameters are completely determined by the asymptotic BH mass and
spin. The ringdown emission is observable in binary black holes (BBH) coalescences by
means of the current and upcoming ground-based interferometers network. Employing
the known general relativistic predictions for the spectrum (both from linearized theory
and complete numerical solutions), it is possible to test for the existence of alternative
extreme compact objects, new particles surrounding BHs, hairy BHs or even wormholes.
In this talk, we present the first experimental implementation of BH spectroscopy,
test for the presence of multiple modes through Bayesian model comparison and
infer the transition time between the non-linear and the quasi-stationary regime of the
post-merger signal. We further place constraints on the excitation amplitudes of ringdown
modes and investigate classical bounds on the information emission rate of BHs.
Finally we show the constraints we can currently place on parametric deviations
from general relativity predictions for the spectrum
and how the increasing sensitivity of the current network of interferometers
will allow precision tests of general relativity in the ringdown regime.