Black-hole hair loss: Learning about binary progenitors from ringdown signals

Perturbed Kerr black holes emit gravitational radiation, which (for the practical purposes of gravitational-wave astronomy) consists of a superposition of damped sinusoids termed quasinormal modes. The frequencies and time constants of the modes depend only on the mass and spin of the black hole-a consequence of the no-hair theorem. It has been proposed that a measurement of two or more quasinormal modes could be used to confirm that the source is a black hole and to test if general relativity continues to hold in ultrastrong gravitational fields. In this paper, we propose a practical approach to testing general relativity with quasinormal modes. We will also argue that the relative amplitudes of the various quasinormal modes encode important information about the origin of the perturbation that caused them. This helps in inferring the nature of the perturbation from an observation of the emitted quasinormal modes. In particular, we will show that the relative amplitudes of the different quasinormal modes emitted in the process of the merger of a pair of nonspinning black holes can be used to measure the component masses of the progenitor binary.