Tests of General Relativity with GWTC-3

TL;DR

GWTC-3 conducts a comprehensive suite of GR tests on O3b gravitational-wave events, targeting generation, propagation, and polarization effects, plus remnant properties. It employs GR-based waveform models (PhenomXPHM, SEOBNRv4), parameterized PN deviations, and hierarchical population analyses to derive stringent constraints. Across 15 high-significance events, including GW200115 (NSBH candidate) and many BBH mergers, the results show no detectable departures from GR: residuals align with noise, IMR remnant inferences are GR-consistent, PN-deformation bounds tighten previous limits, and the graviton-mass bound is updated to m_g ≤ 2.42 × 10^-23 eV/c^2. Ringdown and echoes analyses further support Kerr remnant predictions and show no evidence for ECO-like signatures; polarization tests place no evidence for non-tensor modes. Overall, GWTC-3 strengthens GR’s validity in the dynamical, strong-field regime and imposes robust constraints on broad classes of beyond-GR theories, with population-level bounds improving as the catalog grows.

Abstract

The ever-increasing number of detections of gravitational waves (GWs) 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 $\leq 10^{-3}\, {\rm yr}^{-1}$. In addition to signals consistent with binary black hole (BH) mergers, the new events include GW200115_042309, a signal consistent with a neutron star--BH 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 ~2 in the -1PN parameter. We also find that the spin-induced quadrupole moments of the binary BH constituents are consistent with those of Kerr BHs in GR. We find no evidence for dispersion of GWs, 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 $m_g \leq 2.42 \times 10^{-23} \mathrm{eV}/c^2$. The final mass and final spin as inferred from the pre-merger and post-merger parts of the waveform are consistent with each other. The studies of the properties of the remnant BHs, including deviations of the quasi-normal 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 GW signals to calculate more precise population constraints. We find no evidence in support of physics beyond GR.

Figures (16)

• Figure 1: Results of the residuals analysis (Sec. \ref{['sec:res']}). Scatter plot of the maximum-likelihood template (${\rm SNR}_{\rm GR}$) and the upper limit on the residual network SNR (${\rm SNR}_{90}$) for each event. The colorbar denotes the $p$-values of individual events. Solid (empty) circles represent the O3b (pre-O3b) events. The O3b events with highest (lowest) $p$-values are highlighted by green (purple) diamonds.
• Figure 2: Results of the residuals analysis (Sec. \ref{['sec:res']}). The blue curve shows the fraction of events with $p$-values of the residual SNR less than or equal to the abscissa (PP plot). The light-blue band represents the $90\%$ credible interval of the observed $p$-values. The diagonal dashed line denotes the null hypothesis with the surrounding light-grey area denoting the $90\%$ uncertainty region of the null hypothesis due to the finite number of events.
• Figure 3: Combined results of the IMR consistency test for BBH events which satisfy the selection criteria (see Table \ref{['tab:imrct_params']} and Appendix \ref{['app:imr']}). The combined bounds are obtained assuming the same deviation for all events. The main panel shows the 90% credible regions of the two-dimensional posteriors on $(\Delta M_{\rm f} / \bar{M}_{\rm f}, \Delta \chi_{\rm f} / \bar{\chi}_{\rm f})$ assuming a uniform prior, with $(0,0)$ being the expected value for GR. The side panels show the marginalized posterior on $\Delta M_{\rm f} / \bar{M}_{\rm f}$ and $\Delta \chi_{\rm f} / \bar{\chi}_{\rm f}$. The gray distributions correspond to posteriors obtained by combining individual results. The other colored traces correspond to the O3b events given in Table \ref{['tab:imrct_params']} where the color encodes the median redshifted total mass.
• Figure 4: Distributions on the remnant mass (blue) and spin (red) fractional deviation parameters obtained by hierarchically combining the GWTC-3 events (solid trace). For comparison, we also show the results obtained using GWTC-2 (dot dashed traces) and GWTC-1 (dashed) events. The vertical dashed line shows the GR prediction. Triangles mark the GWTC-3 medians, and vertical bars the symmetric 90%-credible intervals.
• Figure 5: Posteriors on the hyperparameters $\mu$ and $\sigma$ of $\Delta \chi_{\rm f} / \bar{\chi}_{\rm f}$ distribution. The GWTC-2 and GWTC-3 posteriors on $\sigma$ show a marked deviation from zero primarily due to GW190814H191118NGW191118_212859200105FGW200105_162426200121A200121_031748200201FGW200201_203549200214K200214_224526200219K200219_201407200311HGW200311_103121GW190403BGW190403_051519GW190408HGW190408_181802GW190412BGW190412GW190413AGW190413_052954GW190413EGW190413_134308GW190421IGW190421_213856GW190425BGW190425GW190426NGW190426_190642GW190503EGW190503_185404GW190512GGW190512_180714GW190513EGW190513_205428GW190514EGW190514_065416GW190517BGW190517_055101GW190519JGW190519_153544GW190521BGW190521GW190521EGW190521_074359GW190527HGW190527_092055GW190602EGW190602_175927GW190620BGW190620_030421GW190630EGW190630_185205GW190701EGW190701_203306GW190706FGW190706_222641GW190707EGW190707_093326GW190708MGW190708_232457GW190719HGW190719_215514GW190720AGW190720_000836GW190725FGW190725_174728GW190727BGW190727_060333GW190728DGW190728_064510GW190731EGW190731_140936GW190803BGW190803_022701GW190804A190804_083543GW190805JGW190805_211137GW190814HGW190814GW190828AGW190828_063405GW190828BGW190828_065509GW190910BGW190910_112807GW190915KGW190915_235702GW190916KGW190916_200658GW190917BGW190917_114630GW190924AGW190924_021846GW190925JGW190925_232845GW190926CGW190926_050336GW190929BGW190929_012149GW190930A190930_234652GW190930CGW190930_133541GW191103AGW191103_012549GW191105CGW191105_143521GW191109AGW191109_010717GW191113BGW191113_071753GW191126CGW191126_115259GW191127BGW191127_050227GW191129GGW191129_134029GW191204AGW191204_110529GW191204GGW191204_171526GW191215GGW191215_223052GW191216GGW191216_213338GW191219EGW191219_163120GW191222AGW191222_033537GW191230HGW191230_180458GW200112HGW200112_155838GW200115AGW200115_042309GW200128CGW200128_022011GW200129DGW200129_065458GW200202FGW200202_154313GW200208GGW200208_130117GW200208KGW200208_222617GW200209EGW200209_085452GW200210BGW200210_092254GW200216GGW200216_220804GW200219DGW200219_094415GW200220EGW200220_061928GW200220HGW200220_124850GW200224HGW200224_222234GW200225BGW200225_060421GW200302AGW200302_015811GW200306AGW200306_093714GW200308GGW200308_173609GW200311LGW200311_115853GW200316IGW200316_215756GW200322GGW200322_091133 posterior on $\Delta \chi_{\rm f} / \bar{\chi}_{\rm f}$ peaking away from zero. The black trace shows the posteriors for GWTC-3 events excluding GW190814H191118NGW191118_212859200105FGW200105_162426200121A200121_031748200201FGW200201_203549200214K200214_224526200219K200219_201407200311HGW200311_103121GW190403BGW190403_051519GW190408HGW190408_181802GW190412BGW190412GW190413AGW190413_052954GW190413EGW190413_134308GW190421IGW190421_213856GW190425BGW190425GW190426NGW190426_190642GW190503EGW190503_185404GW190512GGW190512_180714GW190513EGW190513_205428GW190514EGW190514_065416GW190517BGW190517_055101GW190519JGW190519_153544GW190521BGW190521GW190521EGW190521_074359GW190527HGW190527_092055GW190602EGW190602_175927GW190620BGW190620_030421GW190630EGW190630_185205GW190701EGW190701_203306GW190706FGW190706_222641GW190707EGW190707_093326GW190708MGW190708_232457GW190719HGW190719_215514GW190720AGW190720_000836GW190725FGW190725_174728GW190727BGW190727_060333GW190728DGW190728_064510GW190731EGW190731_140936GW190803BGW190803_022701GW190804A190804_083543GW190805JGW190805_211137GW190814HGW190814GW190828AGW190828_063405GW190828BGW190828_065509GW190910BGW190910_112807GW190915KGW190915_235702GW190916KGW190916_200658GW190917BGW190917_114630GW190924AGW190924_021846GW190925JGW190925_232845GW190926CGW190926_050336GW190929BGW190929_012149GW190930A190930_234652GW190930CGW190930_133541GW191103AGW191103_012549GW191105CGW191105_143521GW191109AGW191109_010717GW191113BGW191113_071753GW191126CGW191126_115259GW191127BGW191127_050227GW191129GGW191129_134029GW191204AGW191204_110529GW191204GGW191204_171526GW191215GGW191215_223052GW191216GGW191216_213338GW191219EGW191219_163120GW191222AGW191222_033537GW191230HGW191230_180458GW200112HGW200112_155838GW200115AGW200115_042309GW200128CGW200128_022011GW200129DGW200129_065458GW200202FGW200202_154313GW200208GGW200208_130117GW200208KGW200208_222617GW200209EGW200209_085452GW200210BGW200210_092254GW200216GGW200216_220804GW200219DGW200219_094415GW200220EGW200220_061928GW200220HGW200220_124850GW200224HGW200224_222234GW200225BGW200225_060421GW200302AGW200302_015811GW200306AGW200306_093714GW200308GGW200308_173609GW200311LGW200311_115853GW200316IGW200316_215756GW200322GGW200322_091133. See Appendix \ref{['app:imr']} for more information about these deviations. The corresponding hyperparameters of the $\Delta M_{\rm f} / \bar{M}_{\rm f}$ distribution do not show any such deviation.