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Abstract Standardizing the definition of eccentricity is necessary for unambiguous inference of the orbital eccentricity of compact binaries from gravitational wave observations. In previous works, we proposed a definition of eccentricity for systems without spin-precession that relies solely on the gravitational waveform, is applicable to any waveform model, and has the correct Newtonian limit. In this work, we extend this definition to spin-precessing systems. This simple yet effective extension relies on first transforming the waveform from the inertial frame to the coprecessing frame, and then adopting an amplitude and a phase with reduced spin-induced effects. Our method includes a robust procedure for filtering out spin-induced modulations, which become non-negligible in the small eccentricity and large spin-precession regime. Finally, we apply our method to a set of Numerical Relativity and Effective One Body waveforms to showcase its robustness for generic eccentric spin-precessing binaries. We make our method public via Python implementation ingw_eccentricity. 

Abstract The Simulating eXtreme Spacetimes Collaboration’s codeSpECcan now routinely simulate binary black hole mergers undergoing $\sim 25$orbits, with the longest simulations undergoing nearly $\sim 180$orbits. While this sounds impressive, the mismatch between the highest resolutions for this long simulation is $O\left({10}^{-1}\right)$. Meanwhile, the mismatch between resolutions for the more typical simulations tends to be $O\left({10}^{-4}\right)$, despite the resolutions being similar to the long simulations’. In this note, we explain why mismatch alone gives an incomplete picture of code—and waveform—quality, especially in the context of providing waveform templates for LISA and 3G detectors, which require templates with $O\left({10}^3\right)-O\left({10}^5\right)$orbits. We argue that to ready the GW community for the sensitivity of future detectors, numerical relativity groups must be aware of this caveat, and also run future simulations with at least three resolutions to properly assess waveform accuracy. 

The measurement of orbital eccentricity in gravitational-wave (GW) signals will provide unique insights into the astrophysical origin of binary systems, while ignoring eccentricity in waveform models could introduce significant biases in parameter estimation and tests of general relativity. Upcoming LIGO-Virgo-KAGRA observing runs are expected to detect a subpopulation of eccentric signals, making it vital to develop accurate waveform models for eccentric orbits. Here, employing recent analytical results through the third post-Newtonian order, we develop v5: a new time-domain, effective-one-body, multipolar waveform model for eccentric binary black holes with spins aligned (or antialigned) with the orbital angular momentum. Besides the dominant (2, 2) mode, the model includes the (2, 1), (3, 3), (3, 2), (4, 4), and (4, 3) modes. We validate the model’s accuracy by computing its unfaithfulness against 99 (28 public and 71 private) eccentric numerical-relativity (NR) simulations, produced by the Simulating eXtreme Spacetimes Collaboration. Importantly, for NR waveforms with initial GW eccentricities below 0.5, the maximum (2, 2)-mode unfaithfulness across the total mass range $20–200M_{\odot }$is consistently below or close to 1%, with a median value of $\sim 0.02\%$, reflecting an accuracy improvement of approximately an order of magnitude compared to the previous-generation v4 and the state-of-the-art esumalí eccentric model. In the quasi-circular-orbit limit, v5 is in excellent agreement with the highly accurate v5 model. The accuracy, robustness, and speed of v5 make it suitable for data analysis and astrophysical studies. We demonstrate this by performing a set of recovery studies of synthetic NR-signal injections, and parameter-estimation analyses of the events GW150914 and GW190521, which we find to have no eccentricity signatures. 

Abstract Accurate modelling of black hole (BH) binaries is critical to achieve the science goals of gravitational-wave detectors. Modelling such configurations relies strongly on calibration to numerical-relativity (NR) simulations. Binaries on quasi-circular orbits have been widely explored in NR, however, coverage of the broader nine-dimensional parameter space, including orbital eccentricity, remains sparse. This article develops a new procedure to control orbital eccentricity of binary BH (BBH) simulations that enables choosing initial data parameters with precise control over eccentricity and mean anomaly of the subsequent evolution, as well as the coalescence time. We then calculate several sequences of NR simulations that nearly uniformly cover the two-dimensional eccentricity–mean anomaly space for equal mass, non-spinning BBHs. We demonstrate that, for fixed eccentricity, many quantities related to the merger dynamics of BBHs show an oscillatory dependence on mean anomaly. The amplitude of these oscillations scales nearly linearly with the eccentricity of the system. We find that for the eccentricities explored in this work, the magnitude of deviations in various quantities such as the merger amplitude and peak luminosity can approach ∼5% of their quasi-circular value. We use our findings to explain eccentric phenomena reported in other studies. We also show that methods for estimating the remnant mass employed in the effective-one-body approach exhibit similar deviations, roughly matching the amplitude of the oscillations we find in NR simulations. This work is an important step towards a complete description of eccentric BBH mergers, and demonstrates the importance of considering the entire two-dimensional parameter subspace related to eccentricity. 

is a method of reducing computational burden in numerical relativity simulations of binary black holes in situations where there is a good analytical model of the geometry around (one or both of) the objects. Two such scenarios of relevance in gravitational-wave astronomy are (1) the case of mass-disparate systems, and (2) the early inspiral when the separation is still large. Here we illustrate the utility and flexibility of this technique with simulations of the fully self-consistent radiative evolution in the model problem of a scalar charge orbiting a Schwarzschild black hole under the effect of scalar-field radiation reaction. We explore a range of orbital configurations, including inspirals with large eccentricity (which we follow through to the final plunge and ringdown) and hyperbolic scattering. 

Recent efforts to numerically simulate compact objects in alternative theories of gravity have largely focused on the time-evolution equations. Another critical aspect is the construction of constraint-satisfying initial data with precise control over the properties of the systems under consideration. Here, we augment the extended conformal thin sandwich framework to construct quasistationary initial data for black hole systems in scalar Gauss-Bonnet theory and numerically implement it in the open-source p code. Despite the resulting elliptic system being singular at black hole horizons, we demonstrate how to construct numerical solutions that extend smoothly across the horizon. We obtain quasistationary scalar hair configurations in the test-field limit for black holes with linear/angular momentum as well as for black hole binaries. For isolated black holes, we explicitly show that the scalar profile obtained is stationary by evolving the system in time and compare against previous formulations of scalar Gauss-Bonnet initial data. In the case of the binary, we find that the scalar hair near the black holes can be markedly altered by the presence of the other black hole. The initial data constructed here enable targeted simulations in scalar Gauss-Bonnet simulations with reduced initial transients. Published by the American Physical Society2025 

We uncover late-time gravitational-wave tails in fully nonlinear $3+1$dimensional numerical relativity simulations of merging black holes, using the highly accurate p code. We achieve this result by exploiting the strong magnification of late-time tails due to binary eccentricity, recently observed in perturbative evolutions, and showcase here the tail presence in head-on configurations for several mass ratios close to unity. We validate the result through a large battery of numerical tests and detailed comparison with a perturbative evolution, which display striking agreement with full nonlinear ones in the ringdown regime, and very similar tail morphologies. Our results offer yet another confirmation of the highly predictive power of black hole perturbation theory in the presence of a source, even when applied to nonlinear solutions. The late-time tail signal is much more prominent than anticipated until recently, and possibly within reach of gravitational-wave detector measurements, unlocking observational investigations of an additional set of general relativistic predictions on the long-range gravitational dynamics.