Tests of General Relativity with GWTC-3*

Gravitational-wave observations deliver a unique way to perform tests of the general relativity (GR) in the dynamical strong-field regime. The detections of compact binary coalescences by the advanced LIGO and advanced Virgo detectors during the past observing runs have permitted us to perform several tests of general relativity (GR). We detail the various testing GR analyses performed on these events (GWTC-3), focusing on the second part of the third observing run (O3b) of the LIGO and Virgo detectors.  We report results from individual events and the combined results, including the GWTC-2 events wherever appropriate. O3b consists of 15 new events satisfying the selection criteria. From the consistency tests, we find the residual power after subtracting the best-fit template being consistent with the instrumental noise. Also, the final mass and spin estimates obtained separately from the low and high-frequency parts of the gravitational-wave signal were found to agree. Measurements of parametric deviations of post-Newtonian coefficients agreed to GR predictions, with an improvement by a factor of ∼ 2 in the −1PN parameter. The spin-induced quadrupole moment estimates provide consistent results with a binary black hole system. We find no evidence of modified dispersion, extra polarization modes, and post-merger echoes. The tests performed for merger remnant properties provide consistent results. Furthermore, the graviton bound is updated to $1.23\times 10^{-23}eV/c^{2}$ within the 90\% credibility.