arXiv subjects

Leo C. Stein

Publications and source records attributed to Leo C. Stein.

At least 19 recordsLinked to original sources

arXiv2026

NRSur7dq4v2: A multi-domain precessing surrogate model with improved accuracy

Numerical relativity simulations provide the most accurate waveforms for binary black hole coalescences, but are prohibitively expensive for direct use in gravitational-wave data analysis. Surrogate models overcome this cost, and NRSur7dq4 is commonly used in parameter estimation for this reason. However, there is evidence in the literature that NRSur7dq4's accuracy could be improved in the merger-ringdown portion of the waveform, which is particularly important for the analysis of high-mass binary black hole events. Motivated by these observations, we construct NRSur7dq4v2, a multi-domain extension of NRSur7dq4 in which overlapping temporal subdomains allow tighter, independent error control over the inspiral and merger-ringdown portions of the waveform before they are smoothly combined. To assess the new model's performance in the merger-ringdown regime, we infer the mass and spin of the remnant black hole from quasi-normal fits to the ringdown portion of the surrogate waveform. We find that NRSur7dq4v2 produces significantly improved remnant mass and spin estimates, with gains of roughly factors of $3$ to $10$ over NRSur7dq4. Compared to NRSur7dq4, NRSur7dq4v2 also includes modes up to $\ell=5$, includes more accurate modeling of certain subdominant modes, and introduces a runtime model-complexity feature that gives users direct control over the tradeoff between evaluation cost and accuracy. Finally, alongside the model development, we have optimized the gwsurrogate package to achieve a fourfold speedup for precessing surrogates. The resulting precessing surrogates called through gwsurrogate are now slightly faster than their LALSimulation counterparts.

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arXiv2026

Black hole spectroscopy: from theory to experiment

The "ringdown" radiation emitted by oscillating black holes has great scientific potential. By carefully predicting the frequencies and amplitudes of black hole quasinormal modes and comparing them with gravitational-wave data from compact binary mergers we can advance our understanding of the two-body problem in general relativity, verify the predictions of the theory in the regime of strong and dynamical gravitational fields, and search for physics beyond the Standard Model or new gravitational degrees of freedom. We summarize the state of the art in our understanding of black hole quasinormal modes in general relativity and modified gravity, their excitation, and the modeling of ringdown waveforms. We also review the status of LIGO-Virgo-KAGRA ringdown observations, data analysis techniques, and the bright prospects of the field in the era of LISA and next-generation ground-based gravitational-wave detectors.

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arXiv2026

Fixing the center-of-mass frame of numerical relativity waveforms using the post-Newtonian center-of-mass charge

The Bondi--van der Burg--Metzner--Sachs (BMS) frame of gravitational waves produced by numerical relativity (NR) simulations is crucial for building accurate waveform models. A proper comparison of NR waveforms with other models requires fixing the arbitrary BMS frame. In this work we improve the center-of-mass (CoM) frame fixing for quasicircular, nonprecessing binary systems. Past work approximated the CoM motion with just a linear fit. We compute a post-Newtonian result of the boosted CoM charge to also capture its physical out-spiraling oscillations. We show that using the analytical results improves the robustness of the fit parameters -- translation and boost vectors -- to the choice of duration and time of the fitting window. Our analysis demonstrates a maximum improvement in robustness when the window is placed at the center of the inspiral. We quantified this improvement by computing the ratio of variances of fit parameters when the fit window size is varied. The largest improvement in robustness of parameters is by a factor of $\sim 25$ for the boost vector and $\sim 20$ for the translation vector. Finally, we incorporate this method into the BMS frame-fixing routine of the python package $\texttt{scri}$ for waveforms produced with Cauchy-characteristic evolution.

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arXiv2026

Merger remnant and eccentricity dynamics surrogates for eccentric nonspinning black hole binaries

Accurate models of merger remnants are increasingly important for gravitational-wave science, including precision tests of gravity with ringdown, inference of black-hole populations, and modeling hierarchical mergers. For eccentric binaries, remnant mass, spin, and recoil carry nontrivial imprints of eccentricity that are both physically informative and more challenging to model, yet remain less developed than in the quasi-circular case. We present two new models trained on numerical-relativity (NR) simulations of unequal-mass, non-spinning eccentric binary black holes: NRSurE_q4NoSpin_Remnant, which predicts remnant properties, and NRSurE_q4NoSpin_Dynamics, a time-domain surrogate for the evolution of eccentricity and mean anomaly. Both models are trained on NR simulations over a three-dimensional parameter space with mass ratios $q \leq 4$, eccentricity $e < 0.23$, and mean anomaly $\ell \in [0,2π)$ radians, where both $e$ and $\ell$ defined at $t=-1000M$ relative to peak amplitude and $M$ is the total mass. We highlight some applications, including the phenomenological impact of eccentricity on remnant properties and the enhancement or suppression of recoil. We also provide error estimates for all modeled quantities, supporting reliable use in current and future gravitational-wave parameter-estimation analyses. Both models will be made available through open-source codes.

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arXiv2026

Convergence of post-Newtonian for quasi-circular non-precessing comparable mass ratios BBHs

Post-Newtonian (PN) theory provides the analytic foundation for modeling the early inspiral of binary black holes. However, as an asymptotic series, successive PN orders do not necessarily improve agreement with the full nonlinear dynamics. While this has been explored in the extreme-mass-ratio limit, comparable-mass systems most relevant to current observations have not been benchmarked as systematically at high PN order. We study the convergence of the PN series for non-spinning and quasi-circular systems by comparing the PN energy flux at future null infinity to a long, high-accuracy numerical relativity (NR) simulation. To enable a gauge-consistent comparison, we place both descriptions in the same BMS frame and calibrate the intrinsic PN parameters by fitting to the NR waveform in the early inspiral. We find that for orbital velocities $v\lesssim0.45$, higher PN orders continue to reduce the PN--NR flux discrepancy, with (incomplete) 6PN providing the best agreement among the orders considered. The improvement with PN order is non-monotonic with local extrema around 2.5PN and 4PN. This implies that the optimal truncation order of the PN series cannot be identified from the first local minimum in the energy flux residuals, contrary to suggestions in earlier work. As $v$ approaches $\sim 0.5$ near the innermost circular orbit, higher PN orders no longer improve the agreement between NR and PN, indicating a loss of convergence. These results motivate continued high-order PN calculations and clarify the NR accuracy needed to validate them.

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arXiv2026

Action-angle variables of a binary black hole with arbitrary eccentricity, spins, and masses at 1.5 post-Newtonian order

Accurate and efficient modeling of the dynamics of binary black holes (BBHs) is crucial to their detection through gravitational waves (GWs), with LIGO/Virgo/KAGRA, and LISA in the future. Solving the dynamics of a BBH system with arbitrary parameters without simplifications (like orbit- or precession-averaging) in closed form is one of the most challenging problems for the GW community. One potential approach is using canonical perturbation theory which constructs perturbed action-angle variables from the unperturbed ones of an integrable Hamiltonian system. Having action-angle variables of the integrable 1.5 post-Newtonian (PN) BBH system is therefore imperative. In this paper, we continue the work initiated by two of us in arXiv:2012.06586, where we presented four out of five actions of a BBH system with arbitrary eccentricity, masses, and spins, at 1.5PN order. Here we compute the remaining fifth action using a novel method of extending the phase space by introducing unmeasurable phase space coordinates. We detail how to compute all the frequencies, and sketch how to explicitly transform from the action-angle variables to the usual positions and momenta. This analytically solves the dynamics at 1.5PN. This lays the groundwork to analytically solve the conservative dynamics of the BBH system with arbitrary masses, spins, and eccentricity, at higher PN order, by using canonical perturbation theory.

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arXiv2026

Chaos and fractals of the black hole photon ring

The photon ring of a Kerr black hole decomposes into a self-similar hierarchy of subrings. Here, we show that this self-similar structure persists in phase space. Moreover, near the photon shell of bound photon orbits, dynamics are controlled by a Lyapunov exponent $γ$, whose role we highlight by computing the first-return map for light rays close to an unstably bound orbit. Despite an exponential $e^γ$ sensitivity to initial conditions, nearly bound rays do not exhibit chaotic behavior. However, as the background spacetime is deformed away from the Kerr geometry, chaos sets in, with its first onset most visible near strongly resonant bound orbits in the photon shell. We display two animations: one illustrating the emergence of chaos near the photon shell, which results in a fractal phase-space structure, and another exhibiting how this chaotic, fractal, self-similar structure is encoded in the first-return map.

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arXiv2025

Parameter matching between horizon quasi-local and point-particle definitions at 1PN for quasi-circular and non spinning BBH systems in harmonic gauge

We investigate how commonly used parameter definitions in Post-Newtonian (PN) theory compare with those from Numerical Relativity (NR) for binary black hole (BBH) systems. In NR, masses and spins of each companion are measured quasi-locally from apparent horizon geometry, whereas in PN they are attributes of point particles defined via asymptotic matching in body zones. Although these definitions coincide in the infinite-separation limit, they could differ by finite-separation corrections that matter for precision modeling. Working entirely in harmonic gauge, we perform asymptotic matching between each companion's inner zone metric -- obtained from black hole perturbation theory -- and the PN two-body metric, and construct the coordinate transformation that preserves the gauge in the strong field region. We solve perturbatively for the apparent horizon (AH) on a group of harmonic inertial time slice and compute its quasi-local areal mass from the horizon geometry. Then we establish the leading order matching between quasi-local (AH based) and PN (point-particle) parameter definitions in harmonic gauge. We find that on a horizon penetrating harmonic slicing, the AH quasi-local mass agrees with the PN point-particle mass at 1PN order. For generic harmonic slicings that deviate from the horizon penetrating condition by a 1PN order perturbation, the AH mass differs from the PN mass also by a 1PN correction. This parameter matching is crucial for hybridizing PN and NR waveforms and for providing better initial conditions in NR and Cauchy-Characteristic Evolution (CCE) simulations. The framework provides a bridge between different descriptions of BBH systems, and it can be extended to spinning and eccentric cases and more general NR gauges.

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arXiv2025

Length dependence of waveform mismatch: a caveat on waveform accuracy

The Simulating eXtreme Spacetimes Collaboration's code SpEC can now routinely simulate binary black hole mergers undergoing $\sim25$ orbits, with the longest simulations undergoing nearly $\sim180$ orbits. While this sounds impressive, the mismatch between the highest resolutions for this long simulation is $\mathcal{O}(10^{-1})$. Meanwhile, the mismatch between resolutions for the more typical simulations tends to be $\mathcal{O}(10^{-4})$, 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 $\mathcal{O}(10^{3}) - \mathcal{O}(10^{5})$ 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.

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arXiv2025

The SXS Collaboration's third catalog of binary black hole simulations

We present a major update to the Simulating eXtreme Spacetimes (SXS) Collaboration's catalog of binary black hole simulations. Using highly efficient spectral methods implemented in the Spectral Einstein Code (SpEC), we have nearly doubled the total number of binary configurations from 2,018 to 3,756. The catalog now densely covers the parameter space with precessing simulations up to mass ratio $q=8$ and dimensionless spins up to $|\vecχ|\le0.8$ with near-zero eccentricity. The catalog also includes some simulations at higher mass ratios with moderate spin and more than 250 eccentric simulations. We have also deprecated and rerun some simulations from our previous catalog (e.g., simulations run with a much older version of SpEC or that had anomalously high errors in the waveform). The median waveform difference (which is similar to the mismatch) between resolutions over the simulations in the catalog is $4\times10^{-4}$. The simulations have a median of 22 orbits, while the longest simulation has 148 orbits. We have corrected each waveform in the catalog to be in the binary's center-of-mass frame and exhibit gravitational-wave memory. We estimate the total CPU cost of all simulations in the catalog to be 480,000,000 core-hours. We find that using spectral methods for binary black hole simulations is over 1,000 times more efficient than much shorter finite-difference simulations of comparable accuracy. The full catalog is publicly available through the sxs Python package and at https://data.black-holes.org .

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arXiv2025

Actions of spinning compact binaries: Spinning particle in Kerr matched to dynamics at 1.5 post-Newtonian order

The motion of compact binaries is influenced by the spin of their components starting at the 1.5 post-Newtonian (PN) order. On the other hand, in the large mass ratio limit, the spin of the lighter object appears in the equations of motion at first order in the mass ratio, coinciding with the leading gravitational self-force. Frame and gauge choices make it challenging to compare between the two limits, especially for generic spin configurations. We derive novel closed formulas for the gauge-invariant actions and frequencies for the motion of spinning test particles near Kerr black holes. We use this to express the Hamiltonian perturbatively in terms of action variables up to 3PN and compare it with the 1.5 PN action-angle Hamiltonian at finite mass ratios. This allows us to match the actions across both systems, providing a new gauge-invariant dictionary for interpolation between the two limits.

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arXiv2025

GWSurrogate: A Python package for gravitational wave surrogate models

Fast and accurate waveform models are fundamentally important to modern gravitational wave astrophysics, enabling the study of merging compact objects like black holes and neutron stars. However, generating high-fidelity gravitational waveforms through numerical relativity simulations is computationally intensive, often requiring days to months of computation time on supercomputers. Surrogate models provide a practical solution to dramatically accelerate waveform evaluations (typically tens of milliseconds per evaluation) while retaining the accuracy of computationally expensive simulations. The GWSurrogate Python package provides easy access to these gravitational wave surrogate models through a user-friendly interface. Currently, the package supports 16 surrogate models, each varying in duration, included physical effects (e.g., nonlinear memory, tidal forces, harmonic modes, eccentricity, mass ratio range, precession effects), and underlying solution methods (e.g., Effective One Body, numerical relativity, black hole perturbation theory). GWSurrogate models follow the waveform model conventions used by the LIGO-Virgo-Kagra collaboration, making the package immediately suitable for both theoretical studies and practical gravitational wave data analysis. By enabling rapid and precise waveform generation, GWSurrogate serves as a production-level tool for diverse applications, including parameter estimation, template bank generation, and tests of general relativity.

astro-ph.IM↗

arXiv2025

Modeling the BMS transformation induced by a binary black hole merger

Understanding the characteristics of the remnant black hole formed in a binary black hole merger is crucial for conducting gravitational wave astronomy. Typically, models of remnant black holes provide information about their mass, spin, and kick velocity. However, other information related to the supertranslation symmetries of the BMS group, such as the memory effect, is also important for characterizing the final state of the system. In this work, we build a model of the BMS transformation that maps a binary black hole's inspiral frame to the remnant black hole's canonical rest frame. Training data for this model are created using high-precision numerical relativity simulations of quasi-circular systems with mass ratios $q \le 8$ and spins parallel to the orbital angular momentum with magnitudes $χ_{1}, χ_{2} \le 0.8$. We use Gaussian Process Regression to model the BMS transformations over the three-dimensional parameter space $\left(q, χ_{1}^{z}, χ_{2}^{z}\right)$. The physics captured by this model is strictly non-perturbative and cannot be obtained from post-Newtonian approximations alone, as it requires knowledge of the strong nonlinear effects that are sourced during the merger. Apart from providing the first model of the supertranslation induced by a binary black hole merger, we also find that the kick velocities predicted using Cauchy-characteristic evolution waveforms are, on average, $\sim5\%$ larger than the ones obtained from extrapolated waveforms. Our work has broad implications for improving gravitational wave models and studying the large-scale impact of memory, such as on the cosmological background. The fits produced in this work are available through the Python package $\texttt{surfinBH}$ under the name $\texttt{NRSur3dq8BMSRemnant}$.

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arXiv2025

Closed-form solutions of spinning, eccentric binary black holes at 1.5 post-Newtonian order

The closed-form solution of the 1.5 post-Newtonian (PN) accurate binary black hole (BBH) Hamiltonian system has proven to be difficult to obtain for a long time since its introduction in 1966. Closed-form solutions of the PN BBH systems with arbitrary parameters (masses, spins, eccentricity) are required for modeling the gravitational waves (GWs) emitted by them. Accurate models of GWs are crucial for their detection by LIGO/Virgo and LISA. Only recently, two solution methods for solving the BBH dynamics were proposed in arXiv:1908.02927 (without using action-angle variables), and arXiv:2012.06586, arXiv:2110.15351 (action-angle based). This paper combines the ideas laid out in the above articles, fills the missing gaps and provides the two solutions which are fully 1.5PN accurate. We also present a public Mathematica package BBHpnToolkit which implements these two solutions and compares them with a fully numerical treatment. The level of agreement between these solutions provides a numerical verification for all the five actions constructed in arXiv:2012.06586, and arXiv:2110.15351. This paper hence serves as a stepping stone for pushing the action-angle-based solution to 2PN order via canonical perturbation theory.

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arXiv2025

Approximate helical symmetry in compact binaries

The inspiral of a circular, non-precessing binary exhibits an approximate helical symmetry. The effects of eccentricity, precession, and radiation reaction break the exact symmetry. We estimate the failure of this symmetry using the flux of the BMS charge corresponding to helical symmetry carried away by gravitational waves. We analytically compute the helical flux for binaries moving on eccentric orbits and quasi-circular orbits without precession using post-Newtonian theory. The helical flux is non-vanishing at the 0PN order for eccentric orbits as expected. We analytically predict the helical flux to be at a relative 5PN order for quasi-circular non-precessing binaries. This prediction is compared with 113 quasi-circular non-precessing numerical relativity waveforms from the SXS catalog. We find good agreement between analytical and numerical results for quasi-circular non-precessing binaries establishing that helical symmetry starts to break at 5PN for these binaries.

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arXiv2024

Late-time tails in nonlinear evolutions of merging black holes

We uncover late-time gravitational-wave tails in fully nonlinear 3+1 dimensional numerical relativity simulations of merging black holes, using the highly accurate SpEC 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 perturbative evolutions, which display striking agreement with full nonlinear ones. 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 detectors measurements, unlocking observational investigations of an additional set of general relativistic predictions on the long-range gravitational dynamics.

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arXiv2024

Optimizing post-Newtonian parameters and fixing the BMS frame for numerical-relativity waveform hybridizations

Numerical relativity (NR) simulations of binary black holes provide precise waveforms, but are typically too computationally expensive to produce waveforms with enough orbits to cover the whole frequency band of gravitational-wave observatories. Accordingly, it is important to be able to hybridize NR waveforms with analytic, post-Newtonian (PN) waveforms, which are accurate during the early inspiral phase. We show that to build such hybrids, it is crucial to both fix the Bondi-Metzner-Sachs (BMS) frame of the NR waveforms to match that of PN theory, and optimize over the PN parameters. We test such a hybridization procedure including all spin-weighted spherical harmonic modes with $|m|\leq \ell$ for $\ell\leq 8$, using 29 NR waveforms with mass ratios $q\leq 10$ and spin magnitudes $|χ_1|, |χ_2|\leq 0.8$. We find that for spin-aligned systems, the PN and NR waveforms agree very well. The difference is limited by the small nonzero orbital eccentricity of the NR waveforms, or equivalently by the lack of eccentric terms in the PN waveforms. To maintain full accuracy of the simulations, the matching window for spin-aligned systems should be at least 5 orbits long and end at least 15 orbits before merger. For precessing systems, the errors are larger than for spin-aligned cases. The errors are likely limited by the absence of precession-related spin-spin PN terms. Using $10^5\,M$ long NR waveforms, we find that there is no optimal choice of the matching window within this time span, because the hybridization result for precessing cases is always better if using earlier or longer matching windows. We provide the mean orbital frequency of the smallest acceptable matching window as a function of the target error between the PN and NR waveforms and the black hole spins.

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arXiv2024

A Review of Gravitational Memory and BMS Frame Fixing in Numerical Relativity

Gravitational memory effects and the BMS freedoms exhibited at future null infinity have recently been resolved and utilized in numerical relativity simulations. With this, gravitational wave models and our understanding of the fundamental nature of general relativity have been vastly improved. In this paper, we review the history and intuition behind memory effects and BMS symmetries, how they manifest in gravitational waves, and how controlling the infinite number of BMS freedoms of numerical relativity simulations can crucially improve the waveform models that are used by gravitational wave detectors. We reiterate the fact that, with memory effects and BMS symmetries, not only can these next-generation numerical waveforms be used to observe never-before-seen physics, but they can also be used to test GR and learn new astrophysical information about our universe.

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