A no-hair test for binary black holes

One of the consequences of the black-hole “no-hair” theorem in general relativity (GR) is that gravitational radiation (quasinormal modes) from a perturbed Kerr black hole is uniquely determined by its mass and spin. Thus, the spectrum of quasinormal mode frequencies have to be all consistent with the same value of the mass and spin. Similarly, the gravitational radiation from a coalescing binary black hole system is uniquely determined by a small number of parameters (masses and spins of the black holes and orbital parameters). Thus, consistency between different spherical harmonic modes of the radiation is a powerful test that the observed system is a binary black hole predicted by GR. We formulate such a test, develop a Bayesian implementation, demonstrate its performance on simulated data, and investigate the possibility of performing such a test using previous and upcoming gravitational wave observations.