Tests of general relativity with GWTC-3

The ever-increasing number of detections of gravitational waves from compact binaries by the Advanced LIGO and Advanced Virgo detectors allows us to perform ever-more sensitive tests of general relativity (GR) in the dynamical and strong-field regime of gravity. We perform a suite of tests of GR using the compact binary signals observed during the second half of the third observing run of those detectors. We restrict our analysis to the 15 confident signals that have false alarm rates $\ensuremath{\le}{10}^{\ensuremath{-}3}\text{ }\text{ }{\mathrm{yr}}^{\ensuremath{-}1}$. In addition to signals consistent with binary black hole mergers, the new events include GW200115_042309, a signal consistent with a neutron star--black hole merger. We find the residual power, after subtracting the best fit waveform from the data for each event, to be consistent with the detector noise. Additionally, we find all the post-Newtonian deformation coefficients to be consistent with the predictions from GR, with an improvement by a factor of $\ensuremath{\sim}2$ in the $\ensuremath{-}1\mathrm{PN}$ parameter. We also find that the spin-induced quadrupole moments of the binary black hole constituents are consistent with those of Kerr black holes in GR. We find no evidence for dispersion of gravitational waves, non-GR modes of polarization, or post-merger echoes in the events that were analyzed. We update the bound on the mass of the graviton, at 90% credibility, to ${m}_{g}\ensuremath{\le}2.42\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}23}\text{ }\text{ }\mathrm{eV}/{c}^{2}$. The final mass and final spin as inferred from the premerger and postmerger parts of the waveform are consistent with each other. The studies of the properties of the remnant black holes, including deviations of the quasinormal mode frequencies and damping times, show consistency with the predictions of GR. In addition to considering signals individually, we also combine results from the catalog of gravitational waves signals to calculate more precise population constraints. We find no evidence in support of physics beyond general relativity.