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Abstract

One of the consequences of the black-hole "no-hair" theorem in general
relativity (GR) is that gravitational radiation (quasi-normal modes) from a
perturbed Kerr black hole is uniquely determined by its mass and spin. Thus,
the spectrum of quasi-normal 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.