Probing Non-Axisymmetric Violations of the No Hair Theorems with Gravitational Waves

Black holes in general relativity obey the no hair theorems, which has strong implications on the orbital and precessional dynamics of binary black holes. However, this need not be true for black holes in modified theories of gravity, or for exotic compact objects, the latter of which are not necessarily axisymmetric. We here show how non-axisymmetry modifies the precession dynamics of a compact binary inspiral, and consequently, how such effects modify the observed gravitational waveform. We further discuss how well future detectors can constrain such effects through gravitational wave observations of precessing binary black holes.