arXiv subjects

Oliver Long

Publications and source records attributed to Oliver Long.

16 recordsLinked to original sources

arXiv2026

Time-domain framework for the Teukolsky equation with a particle source using comoving hyperboloidal coordinates

We present a scheme and implementation code for time-domain integration of the Teukolsky equation in 1+1 dimensions with a point-particle source, based on comoving, spatially compactified hyperboloidal coordinates. We demonstrate that the scheme evades the problem of nonphysical growing modes that plague some numerical evolution schemes without compactification. Our use of comoving coordinates greatly simplifies the application of jump conditions on the particle's worldline. We develop our method and test its performance for a scalar field on a Schwarzschild background, first for a circular geodesic orbit source and then for a scattering geodesic orbit. We then present a test implementation of the method for the $s = -2$ Teukolsky equation, illustrating its long-term stability and absence of growing-mode behavior through comparison with similar results using noncompactified characteristic coordinates. Our method paves the way to calculations of the full gravitational self-force in extreme-mass-ratio scattering.

gr-qc↗

arXiv2026

Accurate waveforms for generic planar-orbit binary black holes: The multipolar effective-one-body model SEOBNRv6EHM

Accurate and computationally efficient waveform models are required to infer the parameters of compact binaries from their gravitational wave (GW) emission. Among these parameters, orbital eccentricity serves as a smoking gun for dynamical formation channels and must be accounted for to avoid systematic errors in GW analyses. Here, we present SEOBNRv6EHM, a time-domain, multipolar waveform model for binaries on generic planar orbits, calibrated to quasi-circular (QC) numerical-relativity (NR) simulations from the SXS collaboration. In addition to the dominant $(2,2)$ mode, the model provides the $(2,1)$, $(3,3)$, $(3,2)$, $(4,4)$, and $(4,3)$ multipoles for the full inspiral-merger-ringdown process of coalescing binaries, as well as for dynamical captures and scattering encounters. The model is built within the effective-one-body (EOB) framework, and it employs novel resummations of the radiation-reaction force and waveform modes. We validate its accuracy through comparisons against 592 QC, 319 eccentric, one dynamical-capture, and two scattering SXS NR waveforms, and through scattering-angle comparisons against 61 SXS NR simulations. For QC and small-eccentricity binaries, its accuracy is comparable to previous-generation SEOBNRv5 models. For highly eccentric systems, however, SEOBNRv6EHM attains unprecedented accuracy, with waveform mismatches remaining below or close to $ 2\% $ across the total mass range $ 20-200\, \mathrm{M}_\odot $ for eccentricities up to $\sim 0.9$ at 14 periastron passages before merger. Additionally, SEOBNRv6EHM achieves waveform-generation walltimes that are $ 2 - 6 $ times faster than other state-of-the-art EOB eccentric models, enabling efficient and accurate applications in GW astronomy.

gr-qc↗

arXiv2026

Resummed energy loss in extreme-mass-ratio scattering using critical orbits

Motivated by recent efforts to bridge between weak-field and strong-field descriptions of black-hole binary dynamics, we develop a resummation scheme for post-Minkowskian radiative observables in extreme-mass-ratio scattering, augmented with post-Newtonian terms. Specifically, we derive universal interpolation formulas for the total energy emitted in gravitational waves out to infinity and down the event horizon of the large black hole, valid to leading order in the small mass ratio. We test our formulas using numerical results from direct calculations in black hole perturbation theory. The central idea of our approach is to utilize as a strong-field diagnostic the known form of divergence in the radiated energy along geodesics near the parameter-space separatrix between scattering and plunge. The dominant, logarithmic term of this divergence can be expressed in terms of instantaneous energy fluxes calculated along the unstable circular geodesics that form the separatrix, fluxes that we obtain using interpolation of highly accurate numerical data. The same idea could be applied to bound-orbit radiative observables via either unbound-to-bound mapping or a direct resummation of bound-orbit post-Newtonian expressions.

gr-qc↗

arXiv2025

Black-hole scattering with numerical relativity: Self-force extraction and post-Minkowskian validation

The asymptotic nature of unbound binary-black-hole encounters provides a clean method for comparing different approaches for modeling the two-body problem in general relativity. In this work, we use numerical relativity simulations of black-hole scattering, generated using the Spectral Einstein Code, to explore the self-force and post-Minkowskian expansions of the scattering angle. First, we use a set of unequal-mass simulations to extract the self-force contributions to the scattering angle. Our main result is that using information up to second-order in the symmetric mass ratio (2SF) reproduces numerical relativity within the error bars across the full range of mass-ratios, including equal mass. Next, we compare our numerical relativity results to state-of-the-art post-Minkowskian predictions at larger impact parameters than previously explored. We find good agreement in the weak-field regime and discuss the relative importance of higher-order terms.

gr-qc↗

arXiv2025

Frequency-domain self-force calculations using Gegenbauer reconstruction

We investigate the use of the Gegenbauer procedure for time-domain reconstruction in frequency-domain calculations of the self-force on a particle orbiting a black hole. The conventional technique relies on the so-called method of extended homogeneous solutions (EHSs), which circumvents the Gibbs phenomenon that would otherwise hamper the reconstruction of the particle's field from frequency modes. Unfortunately, the effectiveness of EHS reconstruction deteriorates rapidly with increasing orbital eccentricity, due to large numerical cancellations between frequency-mode contributions. Furthermore, the method is only suitable for bound orbits and cannot be fully applied in scattering scenarios. The Gegenbauer reconstruction procedure involves a reprojection of the partial Fourier representation onto a complementary basis of polynomials. The resulting series converges exponentially while averting the cancellation problem. We demonstrate the procedure with numerical results for the spherical harmonic modes of the scalar field sourced by a scalar charge in orbit around a Schwarzschild black hole. We illustrate the merits of this approach, and discuss the challenges that remain for a full Gegenbauer-based self-force calculation.

gr-qc↗

arXiv2025

Parameter control for binary black hole initial data

When numerically solving Einstein's equations for binary black holes (BBH), we must find initial data on a three-dimensional spatial slice by solving constraint equations. The construction of initial data is a multi-step process, in which one first chooses freely specifiable data that define a conformal background and impose boundary conditions. Then, one numerically solves elliptic equations and calculates physical properties such as horizon masses, spins, and asymptotic quantities from the solution. To achieve desired properties, one adjusts the free data in an iterative ``control'' loop. Previous methods for these iterative adjustments rely on Newtonian approximations and do not allow the direct control of total energy and angular momentum of the system, which becomes particularly important in the study of hyperbolic encounters of black holes. Using the $\texttt{SpECTRE}$ code, we present a novel parameter control procedure that benefits from Broyden's method in all controlled quantities. We use this control scheme to minimize drifts in bound orbits and to enable the construction of hyperbolic encounters. We see that the activation of off-diagonal terms in the control Jacobian gives us better efficiency when compared to the simpler implementation in the Spectral Einstein Code ($\texttt{SpEC}$). We demonstrate robustness of the method across extreme configurations, including spin magnitudes up to $\chi = 0.9999$, mass ratios up to $q = 50$, and initial separations up to $D_0 = 1000M$. Given the open-source nature of $\texttt{SpECTRE}$, this is the first time a parameter control scheme for constructing bound and unbound BBH initial data is available to the numerical-relativity community.

gr-qc↗

arXiv2025

Highly accurate simulations of asymmetric black-hole scattering and cross validation of effective-one-body models

The study of unbound binary-black-hole encounters provides a gauge-invariant approach to exploring strong-field gravitational interactions in two-body systems, which can subsequently inform waveform models for bound orbits. In this work, we present 60 new highly accurate numerical relativity (NR) simulations of black-hole scattering, generated using the Spectral Einstein Code (SpEC). Our simulations include 14 spin-aligned configurations, as well as 16 configurations with unequal masses, up to a mass ratio of 10. We perform the first direct comparison of scattering angles computed using different NR codes, finding good agreement. We compare our NR scattering angle results to the post-Minkowskian (PM)-based effective-one-body (EOB) closed-form models SEOB-PM and $w_{\rm EOB}$, finding less than 5% deviation except near the scatter-capture separatrix. Comparisons with the post-Newtonian-based EOB evolution models SEOBNRv5 and TEOBResumS-Dal\'{i} reveal that the former agrees within 8% accuracy with non-spinning NR results across most parameter ranges, whereas the latter matches similarly at lower energies but diverges significantly at higher energies. Both evolution EOB models exhibit increased deviations for spinning systems, predicting a notably different location of the capture separatrix compared to NR. Our key result is the first measurement of disparate scattering angles from NR simulations due to asymmetric gravitational-wave emission. We compare these results to SEOB-PM models constructed to calculate the scattering angle of a single black hole in asymmetric systems.

gr-qc↗

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 $|\vec{\chi}|\le0.8$ 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 .

gr-qc↗

arXiv2024

Black hole scattering near the transition to plunge: Self-force and resummation of post-Minkowskian theory

Geodesic scattering of a test particle off a Schwarzschild black hole can be parameterized by the speed-at-infinity $v$ and the impact parameter $b$, with a "separatrix", $b=b_c(v)$, marking the threshold between scattering and plunge. Near the separatrix, the scattering angle diverges as $\sim\log(b-b_c)$. The self-force correction to the scattering angle (at fixed $v,b$) diverges even faster, like $\sim A_1(v)b_c/(b-b_c)$. Here we numerically calculate the divergence coefficient $A_1(v)$ in a scalar-charge toy model. We then use our knowledge of $A_1(v)$ to inform a resummation of the post-Minkowskian expansion for the scattering angle, and demonstrate that the resummed series agrees remarkably well with numerical self-force results even in the strong-field regime. We propose that a similar resummation technique, applied to a mass particle subject to a gravitational self-force, can significantly enhance the utility and regime of validity of post-Minkowskian calculations for black-hole scattering.

gr-qc↗

arXiv2023

Waveform Modelling for the Laser Interferometer Space Antenna

LISA, the Laser Interferometer Space Antenna, will usher in a new era in gravitational-wave astronomy. As the first anticipated space-based gravitational-wave detector, it will expand our view to the millihertz gravitational-wave sky, where a spectacular variety of interesting new sources abound: from millions of ultra-compact binaries in our Galaxy, to mergers of massive black holes at cosmological distances; from the beginnings of inspirals that will venture into the ground-based detectors' view to the death spiral of compact objects into massive black holes, and many sources in between. Central to realising LISA's discovery potential are waveform models, the theoretical and phenomenological predictions of the pattern of gravitational waves that these sources emit. This white paper is presented on behalf of the Waveform Working Group for the LISA Consortium. It provides a review of the current state of waveform models for LISA sources, and describes the significant challenges that must yet be overcome.

gr-qc↗

arXiv2023

Extending black-hole remnant surrogate models to extreme mass ratios

Numerical-relativity surrogate models for both black-hole merger waveforms and remnants have emerged as important tools in gravitational-wave astronomy. While producing very accurate predictions, their applicability is limited to the region of the parameter space where numerical-relativity simulations are available and computationally feasible. Notably, this excludes extreme mass ratios. We present a machine-learning approach to extend the validity of existing and future numerical-relativity surrogate models toward the test-particle limit, targeting in particular the mass and spin of post-merger black-hole remnants. Our model is trained on both numerical-relativity simulations at comparable masses and analytical predictions at extreme mass ratios. We extend the gaussian-process-regression model NRSur7dq4Remnant, validate its performance via cross validation, and test its accuracy against additional numerical-relativity runs. Our fit, which we dub NRSur7dq4EmriRemnant, reaches an accuracy that is comparable to or higher than that of existing remnant models while providing robust predictions for arbitrary mass ratios.

gr-qc↗

arXiv2023

Hyperboloidal discontinuous time-symmetric numerical algorithm with higher order jumps for gravitational self-force computations in the time domain

Within the next decade the Laser Interferometer Space Antenna (LISA) is due to be launched, providing the opportunity to extract physics from stellar objects and systems, such as \textit{Extreme Mass Ratio Inspirals}, (EMRIs) otherwise undetectable to ground based interferometers and Pulsar Timing Arrays (PTA). Unlike previous sources detected by the currently available observational methods, these sources can \textit{only} be simulated using an accurate computation of the gravitational self-force. Whereas the field has seen outstanding progress in the frequency domain, metric reconstruction and self-force calculations are still an open challenge in the time domain. Such computations would not only further corroborate frequency domain calculations and models, but also allow for full self-consistent evolution of the orbit under the effect of the self-force. Given we have \textit{a priori} information about the local structure of the discontinuity at the particle, we will show how to construct discontinuous spatial and temporal discretisations by operating on discontinuous Lagrange and Hermite interpolation formulae and hence recover higher order accuracy. In this work we demonstrate how this technique in conjunction with well-suited gauge choice (hyperboloidal slicing) and numerical (discontinuous collocation with time symmetric) methods can provide a relatively simple method of lines numerical algorithm to the problem. This is the first of a series of papers studying the behaviour of a point-particle prescribing circular geodesic motion in Schwarzschild in the \textit{time domain}. In this work we describe the numerical machinery necessary for these computations and show not only our work is capable of highly accurate flux radiation measurements but it also shows suitability for evaluation of the necessary field and it's derivatives at the particle limit.

gr-qc↗

arXiv2023

Comparison of post-Minkowskian and self-force expansions: Scattering in a scalar charge toy model

We compare numerical self-force results and analytical fourth-order post-Minkowskian (PM) calculations for hyperbolic-type scattering of a point-like particle carrying a scalar charge $Q$ off a Schwarzschild black hole, showing a remarkably good agreement. Specifically, we numerically compute the scattering angle including the full $O(Q^2)$ scalar-field self-force term (but ignoring the gravitational self-force), and compare with analytical expressions obtained in a PM framework using scattering-amplitude methods. This example provides a nontrivial, high-precision test of both calculation methods, and illustrates the complementarity of the two approaches in the context of the program to provide high-precision models of gravitational two-body dynamics. Our PM calculation is carried out through 4PM order, i.e., including all terms through $O(Q^2 G^3)$. At the fourth post-Minkowskian order the point-particle description involves two a-priori undetermined coefficients, due to contributions from tidal effects in the model under consideration. These coefficients are chosen to align the post-Minkowskian results with the self-force ones.

hep-th↗

arXiv2022

Self-force in hyperbolic black hole encounters

Self-force methods can be applied in calculations of the scatter angle in two-body hyperbolic encounters, working order by order in the mass ratio (assumed small) but with no recourse to a weak-field approximation. This, in turn, can inform ongoing efforts to construct an accurate description of the general-relativistic binary dynamics via an effective-one-body description or other approaches. Existing self-force methods are to a large extent specialised to bound, inspiral orbits. Here we derive the first-order conservative self-force correction to the scattering angle, show its agreement with recent post-Minkowsian results, and develop a technique for (numerical) self-force calculations that can efficiently tackle scatter orbits. In the method, the metric perturbation is reconstructed from a Hertz potential that satisfies (mode-by-mode) a certain inhomogeneous version of the Teukolsky equation. The crucial ingredient in this formulation are certain jump conditions that the (multipole modes of the) Hertz potential must satisfy along the worldline of the small body's orbit. We present a closed-form expression for these jumps, for an arbitrary geodesic orbit in Schwarzschild spacetime. To begin developing the numerical infrastructure, a scalar-field evolution code on a Schwarzschild background (in 1+1D) is developed. Following this, results for the conservative scalar self-force corrections to the scatter angle are calculated. We continue by constructing a Teukolsky evolution code on a Schwarzschild background. This produces numerically unstable solutions due to unphysical homogeneous solutions of the Teukolsky equation at the horizon and null infinity being seeded by numerical error. This can be resolved by a change of variables to a Regge-Wheeler-like field. We then present a full numerical implementation of this method for circular and scatter orbits in Schwarzschild.

gr-qc↗

arXiv2022

Self-force correction to the deflection angle in black-hole scattering: a scalar charge toy model

Using self-force methods, we consider the hyperbolic-type scattering of a pointlike particle carrying a scalar charge $Q$ off a Schwarzschild black hole. For given initial velocity and impact parameter, back-reaction from the scalar field modifies the scattering angle by an amount $\propto\! Q^2$, which we calculate numerically for a large sample of orbits (neglecting the gravitational self-force). Our results probe both strong-field and field-weak scenarios, and in the latter case we find a good agreement with post-Minkowskian expressions. The scalar-field self-force has a component tangent to the four-velocity that exchanges particle's mass with scalar-field energy, and we also compute this mass exchange as a function along the orbit. The expressions we derive for the scattering angle (in terms of certain integrals of the self-force along the orbit) can be used to obtain the gravitational self-force correction to the angle in the physical problem of a binary black hole with a large mass ratio. We discuss the remaining steps necessary to achieve this goal.

gr-qc↗

arXiv2021

Time-domain metric reconstruction for hyperbolic scattering

Self-force methods can be applied in calculations of the scatter angle in two-body hyperbolic encounters, working order by order in the mass ratio (assumed small) but with no recourse to a weak-field approximation. This, in turn, can inform ongoing efforts to construct an accurate model of the general-relativistic binary dynamics via an effective-one-body description and other semi-analytical approaches. Existing self-force methods are to a large extent specialised to bound, inspiral orbits. Here we develop a technique for (numerical) self-force calculations that can efficiently tackle scatter orbits. The method is based on a time-domain reconstruction of the metric perturbation from a scalar-like Hertz potential that satisfies the Teukolsky equation, an idea pursued so far only for bound orbits. The crucial ingredient in this formulation are certain jump conditions that (each multipole mode of) the Hertz potential must satisfy along the orbit, in a 1+1-dimensional multipole reduction of the problem. We obtain a closed-form expression for these jumps, for an arbitrary geodesic orbit in Schwarzschild spacetime, and present a full numerical implementation for a scatter orbit. In this paper we focus on method development, and go only as far as calculating the Hertz potential; a calculation of the self-force and its physical effects on the scatter orbit will be the subject of forthcoming work.

gr-qc↗