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We present a comprehensive assessment of multiparameter tests of general relativity (GR) in the inspiral regime of compact binary coalescences using principal component analysis (PCA). Our analysis is based on an extensive set of simulated gravitational-wave (GW) signals, including both general relativistic and non-GR sources, injected into zero-noise data colored by the noise power spectral densities of the LIGO and Virgo GW detectors at their designed sensitivities. We evaluate the performance of PCA-based methods in the context of two established frameworks: and . For GR-consistent signals, we find that PCA enables stringent constraints on potential deviations from GR, even in the presence of multiple free parameters. Applying the method to simulated signals that explicitly violate GR, we demonstrate that PCA is effective at identifying such deviations. We further test the method using numerical relativity waveforms of eccentric binary black hole systems and show that missing physical effects—such as orbital eccentricity—can lead to apparent violations of GR if not properly included in the waveform models used for analysis. Finally, we apply our PCA-based test to selected real gravitational-wave events from GWTC-3, including GW190814 and GW190412. We present joint constraints from selected binary black hole events in GWTC-3, finding that the 90% credible bound on the most informative PCA parameter is ${0.03}_{-0.08}^{+0.08}$in the framework and $-0.01_{-0.04}^{+0.05}$in the framework, both of which are consistent with GR. These results highlight the sensitivity and robustness of the PCA-based approach and demonstrate its readiness for application to future observational data from the fourth observing runs of LIGO, Virgo, and KAGRA. 

The response of black holes to small perturbations is known to be partially described by a superposition of quasinormal modes. Despite their importance to enable strong-field tests of gravity, little to nothing is known about what overtones and quasinormal-mode amplitudes are like for black holes in extensions to general relativity. We take a first step in this direction and study what is arguably the simplest model that allows first-principle calculations to be made: a nonrotating black hole in an effective-field-theory extension of general relativity with cubic-in-curvature terms. Using a phase-amplitude scheme that uses analytical continuation and the Prüfer transformation, we numerically compute, for the first time, the quasinormal overtone frequencies (in this theory) and quasinormal-mode excitation factors (in any theory beyond general relativity). We find that the overtone quasinormal frequencies and their excitation factors are more sensitive than the fundamental mode to the length scale $l$introduced by the higher-derivative terms in the effective field theory. We argue that a description of all overtones cannot be made within the regime of validity of the effective field theory, and we conjecture that this is a general feature of any extension to general relativity that introduces a new length scale. We also find that a parametrization of the modifications to the general-relativistic quasinormal frequencies in terms of the ratio between $l$and the black hole’s mass is somewhat inadequate, and we propose a better alternative. As an application, we perform a preliminary study of the implications of the breakdown, in the effective field theory, of the equivalence between the quasinormal mode spectra associated to metric perturbations of polar and axial parity of the Schwarzschild black hole in general relativity. We also present a simple justification for the loss of isospectrality. Published by the American Physical Society2024