by Sebastian H. Völkel and Enrico Barausse

Theories of gravity extending or modifying general relativity typically allow for black hole solutions different from the Schwarzschild/Kerr geometries. Electromagnetic observations have been used to place constraints on parametrized deviations from the Schwarzschild/Kerr metrics, in an effort to gain insight on the underlying gravitational theory. In this work, we show that observations of the gravitational quasi-normal modes by existing and future interferometers can be used to bound the same parametrized black hole metrics that are constrained by electromagnetic observations. We argue that our technique is most sensitive to changes in the background black hole metric near the circular photon orbit, and that it is robust against the changes that a gravitational theory differing from general relativity necessarily introduces in the equations for the gravitational perturbations.We demonstate our approach by reconstructing the background metric from a set of simulated observations using a Bayesian approach. We also comment on possible synergies between gravitational wave observations of quasi-normal modes and the operations of the Event Horizon Telescope.