# Searching for black-hole hair with gravitational-wave overtones

*Binary* black hole spectroscopy analyses the entire coalescence signal to test general relativity

According to the no-hair theorem, every stationary astrophysical black hole can be described entirely by just two parameters (its mass and spin). The gravitational waves emitted from perturbed black holes in binary mergers are related to the no-hair theorem. It predicts the emission of multiple damped (quasinormal) modes, the frequencies and damping times of which are uniquely defined by the black hole’s mass and spin. Separately determining the mass and spin from each of the modes and comparing them therefore allows for a test of the no-hair theorem through *black hole spectroscopy*. Now, AEI researchers have implemented a novel scheme for such a test in which they perform *binary* black hole spectroscopy by analysing a decomposition of the entire gravitational-wave signal emitted throughout the inspiral and merger instead of only that emitted after the merger. They apply their test to GW190412 and GW190814 and find no significant deviations from general relativity and therefore no violations of the no-hair theorem.

## Paper abstract

Gravitational waves provide a window to probe general relativity (GR) under extreme conditions. The recent observations of GW190412 and GW190814 are unique high-mass-ratio mergers that enable the observation of gravitational-wave harmonics beyond the dominant (ℓ,m)=(2,2) mode. Using these events, we search for physics beyond GR by allowing the source parameters measured from the subdominant harmonics to deviate from that of the dominant mode. All results are consistent with GR. We constrain the chirp mass as measured by the (ℓ,m)=(3,3) mode to be within 0^{+5}_{−3}% of the dominant mode when we allow both the masses and spins of the subdominant modes to deviate. If we allow only the mass parameters to deviate, we constrain the chirp mass of the (3,3) mode to be within ±1% of the expected value from GR.