Black Hole Spectroscopy and Tests of General Relativity with GW250114

Abstract: The binary black hole signal GW250114, the loudest gravitational wave detected to date, offers a unique opportunity to test Einstein's general relativity (GR) in the high-velocity, strong-gravity regime and probe whether the remnant conforms to the Kerr metric. Upon perturbation, black holes emit a spectrum of damped sinusoids with specific, complex frequencies. Our analysis of the post-merger signal shows that at least two quasi-normal modes are required to explain the data, with the most damped remaining statistically significant for about one cycle. We probe the remnant's Kerr nature by constraining the spectroscopic pattern of the dominant quadrupolar ($\ell = m = 2$) mode and its first overtone to match the Kerr prediction to tens of percent at multiple post-peak times. The measured mode amplitudes and phases agree with a numerical-relativity simulation having parameters close to GW250114. By fitting a parameterized waveform that incorporates the full inspiral-merger-ringdown sequence, we constrain the fundamental $(\ell=m=4)$ mode to tens of percent and bound the quadrupolar frequency to within a few percent of the GR prediction. We perform a suite of tests -- spanning inspiral, merger, and ringdown -- finding constraints that are comparable to, and in some cases 2-3 times more stringent than those obtained by combining dozens of events in the fourth Gravitational-Wave Transient Catalog. These results constitute the most stringent single-event verification of GR and the Kerr nature of black holes to date, and outline the power of black-hole spectroscopy for future gravitational-wave observations.