Scientists with the LIGO–Virgo–KAGRA (LVK) collaboration tested Einstein’s general relativity (GR) using a large set of gravitational‑wave (GW) signals and found no evidence that the theory fails. The team analyzed 168 confident binary merger events from the combined observing runs up to the second part of the fourth run (O4b) and report that the observations are consistent with GR’s predictions within the current measurement limits.

The researchers restricted their study to events seen by at least two detectors and with estimated false‑alarm rates no larger than 10−3 per year (a condition used to select reliable signals). That sample includes 72 events from O4b plus five additional events from the first half of O4 that passed updated search checks, together with earlier detections. For each event they subtracted the best‑fit GR waveform from the data and examined the leftover signal; these residuals are consistent with the detectors’ noise for all events considered. They also searched for gravitational‑wave polarizations beyond the two allowed in GR and found no strong evidence for extra polarization types.

The paper reports seven distinct tests of GR. One set of tests looks at the waves’ generation during the inspiral phase by allowing the so‑called post‑Newtonian (PN) coefficients — numbers that appear in the formulas describing the slow inspiral of two compact objects — to deviate from their GR values. These constraints improved over the previous catalog by factors of about 1.2 to 2.6. The analysis used competing waveform models (named IMRPhenomXPHMSpinTaylor and SEOBNRv5HMROM in the technical literature) to check robustness. A single loud event, GW250114, with a network matched‑filter signal‑to‑noise ratio of 76.9, contributed strongly to tightening these bounds.

Another important class of tests probes the remnant black hole after merger by studying the ringdown — the dying oscillations described by quasi‑normal modes (QNM). The team applied time‑domain and frequency‑domain methods. For GW240621_195059 the post‑merger data are consistent with the dominant quadrupole mode (written l = |m| = 2) of a spinning Kerr black hole and its first overtone. However, some spurious high‑frequency content in the data prevented a clean “spectroscopic” measurement of the mode frequencies for that event. In the frequency‑domain ringdown analysis, the GR prediction lies in the tails of the combined result, which the authors say may be due to the limited size of the catalog. Overall the combined ringdown tests show improved agreement with GR compared with the previous catalog largely because of GW250114.