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Abstract The observation of gravitational waves from compact binary coalescences is a promising tool to test the validity of general relativity (GR) in a highly dynamical strong-field regime. There are now a variety of tests of GR performed on the observed compact binary signals. In this paper, we propose a new test of GR that compares the results of these individual tests. This meta inspiral–merger–ringdown consistency test (IMRCT) involves inferring the final mass and spin of the remnant black hole obtained from the analyses of two different tests of GR and checking for consistency. If there is a deviation from GR, we expect that different tests of GR will recover different values for the final mass and spin, in general. We check the performance of the meta IMRCT using a standard set of null tests used in various gravitational-wave analyses: the original IMRCT, the test infrastructure for GR, the flexible-theory-independent test, and the modified dispersion test. However, the meta IMRCT is applicable to any tests of GR that infer the initial masses and spins or the final mass and spin, including ones that are applied to binary neutron star or neutron star–black hole signals. We apply the meta IMRCT to simulated quasi-circular GR and non-GR binary black hole (BBH) signals as well as to eccentric BBH signals in GR (analysed with quasicircular waveforms). We find that the meta IMRCT gives consistency with GR for the quasi-circular GR signals and picks up a deviation from GR in the other cases, as do other tests. In some cases, the meta IMRCT finds a significant GR deviation for a given pair of tests (and specific testing parameters) while the individual tests do not, showing that it is more sensitive than the individual tests to certain types of deviations. In addition, we also apply this test to a few selected real compact binary signals and find them consistent with GR. 

Abstract We propose a Bayesian inference framework to predict the merger history of LIGO-Virgo binary black holes (BHs), whose binary components may have undergone hierarchical mergers in the past. The framework relies on numerical relativity predictions for the mass, spin, and kick velocity of the remnant BHs. This proposed framework computes the masses, spins, and kicks imparted to the remnant of the parent binaries, given the initial masses and spin magnitudes of the binary constituents. We validate our approach by performing an “injection study” based on a constructed sequence of hierarchically formed binaries. Noise is added to the final binary in the sequence, and the parameters of the “parent” and “grandparent” binaries in the merger chain are then reconstructed. This method is then applied to three GWTC-3 events: GW190521, GW200220_061928, and GW190426_190642. These events were selected because at least one of the binary companions lies in the putative pair-instability supernova mass gap, in which stellar processes alone cannot produce BHs. Hierarchical mergers offer a natural explanation for the formation of BHs in the pair-instability mass gap. We use the backward evolution framework to predict the parameters of the parents of the primary companion of these three binaries. For instance, the parent binary of GW190521 has masses ${72}_{-22}^{+32}{M}_{\odot }$and ${31}_{-23}^{+24}{M}_{\odot }$within the 90% credible interval. Astrophysical environments with escape speeds ≥100 km s⁻¹are preferred sites to host these events. Our approach can be readily applied to future high-mass gravitational wave events to predict their formation history under the hierarchical merger assumption. 

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 most general bound binary black hole system has an eccentric orbit and precessing spins. The detection of such a system with significant eccentricity close to the merger would be a clear signature of dynamical formation. In order to study such systems, it is important to be able to evolve their spins and eccentricity from the larger separations at which the binary formed to the smaller separations at which it is detected, or vice versa. Knowledge of the precessional evolution of the binary’s orbital angular momentum can also be used to twist up aligned-spin eccentric waveform models to create a spin-precessing eccentric waveform model. In this paper, we present a new publicly available code to evolve eccentric, precessing binary black holes using orbit-averaged post-Newtonian (PN) equations from the literature. The spin-precession dynamics is 2PN accurate, i.e., with the leading spin-orbit and spin-spin corrections. The evolution of orbital parameters (orbital frequency, eccentricity, and periastron precession), which follow the quasi-Keplerian parametrization, is 3PN accurate in the point particle terms and includes the leading order spin-orbit and spin-spin effects. All the spin-spin terms include the quadrupole-monopole interaction. The eccentricity enhancement functions in the fluxes use the high-accuracy hyperasymptotic expansions from Loutrel and Yunes []. We discuss various features of the code and study the evolution of the orbital and spin-precession parameters of eccentric, precessing binary black holes. In particular, we study the dependence of the spin morphologies on eccentricity, where we find that the transition point from one spin morphology to another can depend nonmonotonically on eccentricity, and the fraction of binaries in a given morphology at a given point in the evolution of a population depends on the instantaneous eccentricity. 

Black holes (BHs) with masses between $\sim 3–5M_{\odot }$, produced by a binary neutron star (BNS) merger, can further pair up with a neutron star or BH and merge again within a Hubble time. However, the astrophysical environments in which this can happen and the rate of such mergers are open questions in astrophysics. Gravitational waves may play an important role in answering these questions. In this context, we discuss the possibility that the primary of the recent LIGO-Virgo-KAGRA binary GW230529_181500 (GW230529, in short) is the product of a previous BNS merger. Invoking numerical relativity (NR)-based fitting formulas that map the binary constituents’ masses and tidal deformabilities to the mass, spin, and kick velocity of the remnant BH, we investigate the potential parents of GW230529’s primary. Our calculations using NR fits based on BNS simulations reveal that the remnant of a high-mass BNS merger similar to GW190425 is consistent with the primary of GW230529. This argument is further strengthened by the gravitational wave-based merger rate estimation of GW190425-like and GW230529-like populations. We show that around 18% (median) of the GW190425-like remnants could become the primary component in GW230529-like mergers. The dimensionless tidal deformability parameter of the heavier neutron star in the parent binary is constrained to ${67}_{-61}^{+163}$at 90% credibility. Using estimates of the gravitational-wave kick imparted to the remnant, we also discuss the astrophysical environments in which these types of mergers can take place and the implications for their future observations. 

General relativity (GR) has proven to be a highly successful theory of gravity since its inception. The theory has thrivingly passed numerous experimental tests, predominantly in weak gravity, low relative speeds, and linear regimes, but also in the strong-field and very low-speed regimes with binary pulsars. Observable gravitational waves (GWs) originate from regions of spacetime where gravity is extremely strong, making them a unique tool for testing GR, in previously inaccessible regions of large curvature, relativistic speeds, and strong gravity. Since their first detection, GWs have been extensively used to test GR, but no deviations have been found so far. Given GR’s tremendous success in explaining current astronomical observations and laboratory experiments, accepting any deviation from it requires a very high level of statistical confidence and consistency of the deviation across GW sources. In this paper, we compile a comprehensive list of potential causes that can lead to a false identification of a GR violation in standard tests of GR on data from current and future ground-based GW detectors. These causes include detector noise, signal overlaps, gaps in the data, detector calibration, source model inaccuracy, missing physics in the source and in the underlying environment model, source misidentification, and mismodeling of the astrophysical population. We also provide a rough estimate of when each of these causes will become important for tests of GR for different detector sensitivities. We argue that each of these causes should be thoroughly investigated, quantified, and ruled out before claiming a GR violation in GW observations. 

The production of black holes with masses between ∼50⁢𝑀⊙−130⁢𝑀⊙ is believed to be prohibited by stellar processes due to (pulsational) pair-instability supernovae. Hierarchical mergers of black holes in dense star clusters are proposed as a mechanism to explain the observations of binary black holes with component masses in this range by LIGO/Virgo. We study the efficiency with which hierarchical mergers can produce higher and higher masses using a simple model of the forward evolution of binary black hole populations in gravitationally bound systems like stellar clusters. The model relies on pairing probability and initial mass functions for the black hole population, along with numerical relativity fitting formulas for the mass, spin, and kick speed of the merger remnant. We carry out an extensive comparison of the predictions of our model with clusterBHBdynamics (cBHBD) model, a fast method for the evolution of star clusters and black holes therein. For this comparison, we consider three different pairing functions of black holes and consider simulations from high- and low-metallicity cluster environments from cBHBD. We find good agreements between our model and the cBHBD results when the pairing probability of binaries depends on both total mass and mass ratio. We also assess the efficiency of hierarchical mergers as a function of merger generation and derive the mass distribution of black holes using our model. We find that the multimodal features in the observed binary black hole mass spectrum—revealed by the nonparametric population models—can be interpreted by invoking the hierarchical merger scenario in dense, metal-rich, stellar environments. Further, the two subdominant peaks in the GWTC-3 component mass spectrum are consistent with second and third-generation mergers in metal-rich, dense environments. With more binary black hole detections, our model could be used to infer the black hole initial mass function and pairing probability exponents. 

Amplitude and phase of the gravitational waveform from compact binary systems can be decomposed in terms of their mass- and current-type multipole moments. In a modified theory of gravity, one or more of these multipole moments could deviate from general theory of relativity. In this work, we show that a waveform model that parametrizes the amplitude and phase in terms of the multipole moments of the binary can facilitate a novel multiparameter test of general relativity with exquisite precision. Using a network of next-generation gravitational-wave observatories, simultaneous deviation in the leading seven multipoles of a GW190814-like binary can be bounded to within 6%–40% depending on the multipole order, while supermassive black hole mergers observed by the Laser Interferometer Space Antenna achieve a bound of 0.3%–2%. We further argue that bounds from multipoles can be uniquely mapped onto other parametrized tests of general relativity and have the potential to become a downstream analysis from which bounds of other parametric tests of general relativity can be derived. The set of multipole parameters, therefore, provides an excellent basis to carry out precision tests of general relativity. 

The spin orientations of spinning binary black hole (BBH) mergers detected by ground-based gravitational wave detectors such as LIGO and Virgo can provide important clues about the formation of such binaries. However, these spin tilts, i.e., the angles between the spin vector of each black hole and the binary’s orbital angular momentum vector, can change due to precessional effects as the black holes evolve from a large separation to their merger. The tilts inferred at a frequency in the sensitive band of the detectors by comparing the signal with theoretical waveforms can thus be significantly different from the tilts when the binary originally formed. These tilts at the binary’s formation are well approximated in many scenarios by evolving the BBH backward in time to a formally infinite separation. Using the tilts at infinite separation also places all binaries on an equal footing in analyzing their population properties. In this paper, we perform parameter estimation for simulated BBHs and investigate the differences between the tilts one infers directly close to merger and those obtained by evolving back to infinite separation. We select simulated observations such that their configurations show particularly large differences in their orientations close to merger and at infinity. While these differences may be buried in the statistical noise for current detections, we show that in future plus-era (A+ and Virgo+) detectors, they can be easily distinguished in some cases. We also consider the tilts at infinity for BBHs in various spin morphologies and at the endpoint of the up-down instability. In particular, we find that we are able to easily identify the up-down instability cases as such from the tilts at infinity. 

We present, for the first time, recoil velocity estimates for binary neutron star mergers using data from numerical relativity simulations. We find that binary neutron star merger remnants can have recoil velocity of the order of a few tens of kilometers per second and as high as 150 kilometers per second in our dataset. These recoils are attained due to equivalent contributions from the anisotropic gravitational wave emission as well as the asymmetric ejection of dynamical matter during the merger. We provide fits for net recoil velocity as well as its ejecta component as a function of the amount of ejected matter, which may be useful when constraints on the ejected matter are obtained through electromagnetic observations. We also estimate the mass and spin of the remnants and find them to be in the range [2.34, 3.38]M⊙ and [0.63, 0.82], respectively, for our dataset.