arXiv subjects

Leor Barack

Publications and source records attributed to Leor Barack.

At least 19 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

LISA science ground segment conventions

This document sets out the conventions used for data simulations, waveforms, and analysis pipelines within the Distributed Data Processing Centre (DDPC) of the Laser Interferometer Space Antenna (LISA). It can also be considered a best practice guide for all publications related to the LISA mission. Topics covered include time-to-frequency transformations, gravitational-wave source parametrization, the instrumental response to gravitational waves, time-delay interferometry, and reference frame definitions.

astro-ph.IM↗

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

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

Effective source for second-order self-force calculations: quasicircular orbits in Schwarzschild spacetime

Recent years have seen the first production of "post-adiabatic" gravitational-waveform models based on second-order gravitational self-force theory. These models rely on calculations of an effective source in the perturbative second-order Einstein equation. Here, for the first time, we detail the calculation of the effective source in a Schwarzschild background, which underlies the second-order self-force results in [Phys. Rev. Lett. 127, 151102 (2021); ibid. 128, 231101 (2022); ibid. 130, 241402 (2023)]. The source is designed for use in the multiscale form of the Lorenz-gauge Einstein equation, decomposed in tensor spherical harmonics, or in the analogous second-order Teukolsky equation. It involves, among other things, contributions from (i) quadratic coupling of first-order field modes, (ii) the slow evolution of first-order fields, (iii) quadratic products of a first-order puncture field, and (iv) the second-order puncture field. We validate each of these pieces through numerical and analytical tests.

gr-qc↗

arXiv2024

Premerger observation and characterization of massive black hole binaries

We demonstrate an end-to-end technique for observing and characterizing massive black hole binary signals before they merge with the LISA space-based gravitational-wave observatory. Our method uses a zero-latency whitening filter, originally designed for rapidly observing compact binary mergers in ground-based observatories, to be able to observe signals with no additional latency due to filter length. We show that with minimal computational cost, we are able to reliably observe signals as early as 14 days premerger as long as the signal has accrued a signal-to-noise ratio of at least 8 in the LISA data. We also demonstrate that this method can be used to characterize the source properties, providing early estimates of the source's merger time, chirp mass, and sky localization. Early observation and characterization of massive black holes is crucial to enable the possibility of rapid multimessenger observations, and to ensure that LISA can enter a protected operating period when the merger signal arrives.

hep-ex↗

arXiv2024

Relieving scale disparity in binary black hole simulations

Worldtube excision 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.

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↗

arXiv2024

Worldtube excision method for intermediate-mass-ratio inspirals: self-consistent evolution in a scalar-charge model

This is a third installment in a program to develop a method for alleviating the scale disparity in binary black hole simulations with mass ratios in the intermediate astrophysical range, where simulation cost is prohibitive while purely perturbative methods may not be adequate. The method is based on excising a "worldtube" around the smaller object, much larger than the object itself, replacing it with an analytical model that approximates a tidally deformed black hole. Previously (arXiv:2304.05329) we have tested the idea in a toy model of a scalar charge in a fixed circular geodesic orbit around a Schwarzschild black hole, solving for the massless Klein-Gordon field in 3+1 dimensions on the SpECTRE platform. Here we take the significant further step of allowing the orbit to evolve radiatively, in a self-consistent manner, under the effect of back-reaction from the scalar field. We compute the inspiral orbit and the emitted scalar-field waveform, showing a good agreement with perturbative calculations in the adiabatic approximation. We also demonstrate how our simulations accurately resolve post-adiabatic effects (for which we do not have perturbative results). In this work we focus on quasi-circular inspirals. Our implementation will shortly be publicly accessible in the SpECTRE numerical relativity code.

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

Frequency-domain approach to self-force in hyperbolic scattering

We develop a frequency-domain method for calculating the self-force acting on a scalar charge on a fixed scattering geodesic in Schwarzschild spacetime. Existing frequency-domain methods, which are tailored for bound orbits, are inadequate here for several reasons. One must account for the continuous spectrum in the scattering problem, deal with slowly-convergent radial integrals that are hard to evaluate numerically, and confront the inapplicability of the standard self-force method of "extended homogeneous solutions", which only works for compactly supported sources. We tackle each of these issues in turn, and then present a full numerical implementation, in which we calculate the self-force correction to the scatter angle due to scalar-field back-reaction. We perform a range of internal validation tests, as well as ones based on comparison with existing time-domain results. We discuss the merits and remaining limitations of our method, and outline directions for future work.

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↗

arXiv2023

Worldtube excision method for intermediate-mass-ratio inspirals: scalar-field model in 3+1 dimensions

Binary black hole simulations become increasingly more computationally expensive with smaller mass ratios, partly because of the longer evolution time, and partly because the lengthscale disparity dictates smaller time steps. The program initiated by Dhesi et al. (arXiv:2109.03531) explores a method for alleviating the scale disparity in simulations with mass ratios in the intermediate astrophysical range ($10^{-4} \lesssim q \lesssim 10^{-2}$), where purely perturbative methods may not be adequate. A region ("worldtube") much larger than the small black hole is excised from the numerical domain, and replaced with an analytical model approximating a tidally deformed black hole. Here we apply this idea to a toy model of a scalar charge in a fixed circular geodesic orbit around a Schwarzschild black hole, solving for the massless Klein-Gordon field. This is a first implementation of the worldtube excision method in full 3+1 dimensions. We demonstrate the accuracy and efficiency of the method, and discuss the steps towards applying it for evolving orbits and, ultimately, in the binary black-hole scenario. Our implementation is publicly accessible in the SpECTRE numerical relativity code.

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

Worldtube excision method for intermediate-mass-ratio inspirals: scalar-field toy model

The computational cost of inspiral and merger simulations for black-hole binaries increases in inverse proportion to the square of the mass ratio $q:=m_2/m_1\leq 1$. One factor of $q$ comes from the number of orbital cycles, which is proportional to $1/q$, and another is associated with the required number of time steps per orbit, constrained (via the Courant-Friedrich-Lewy condition) by the need to resolve the two disparate length scales. This problematic scaling makes simulations progressively less tractable at smaller $q$. Here we propose and explore a method for alleviating the scale disparity in simulations with mass ratios in the intermediate astrophysical range ($10^{-4} \lesssim q\lesssim 10^{-2}$), where purely perturbative methods may not be adequate. A region of radius much larger than $m_2$ around the smaller object is excised from the numerical domain, and replaced with an analytical model approximating a tidally deformed black hole. The analytical model involves certain a priori unknown parameters, associated with unknown bits of physics together with gauge-adjustment terms; these are dynamically determined by matching to the numerical solution outside the excision region. In this paper we develop the basic idea and apply it to a toy model of a scalar charge in a circular geodesic orbit around a Schwarzschild black hole, solving for the massless Klein-Gordon field in a 1+1D framework. Our main goal here is to explore the utility and properties of different matching strategies, and to this end we develop two independent implementations, a finite-difference one and a spectral one. We discuss the extension of our method to a full 3D numerical evolution and to gravity.

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↗

arXiv2021

Discontinuous collocation methods and gravitational self-force applications

Numerical simulations of extereme mass ratio inspirals, the mostimportant sources for the LISA detector, face several computational challenges. We present a new approach to evolving partial differential equations occurring in black hole perturbation theory and calculations of the self-force acting on point particles orbiting supermassive black holes. Such equations are distributionally sourced, and standard numerical methods, such as finite-difference or spectral methods, face difficulties associated with approximating discontinuous functions. However, in the self-force problem we typically have access to full a-priori information about the local structure of the discontinuity at the particle. Using this information, we show that high-order accuracy can be recovered by adding to the Lagrange interpolation formula a linear combination of certain jump amplitudes. We construct discontinuous spatial and temporal discretizations by operating on the corrected Lagrange formula. In a method-of-lines framework, this provides a simple and efficient method of solving time-dependent partial differential equations, without loss of accuracy near moving singularities or discontinuities. This method is well-suited for the problem of time-domain reconstruction of the metric perturbation via the Teukolsky or Regge-Wheeler-Zerilli formalisms. Parallel implementations on modern CPU and GPU architectures are discussed.

math.NA↗

arXiv2019

Self-force effects on the marginally bound zoom-whirl orbit in Schwarzschild spacetime

For a Schwarzchild black hole of mass $M$, we consider a test particle falling from rest at infinity and becoming trapped, at late time, on the unstable circular orbit of radius $r=4GM/c^2$. When the particle is endowed with a small mass, $μ\ll M$, it experiences an effective gravitational self-force, whose conservative piece shifts the critical value of the angular momentum and the frequency of the asymptotic circular orbit away from their geodesic values. By directly integrating the self-force along the orbit (ignoring radiative dissipation), we numerically calculate these shifts to $O(μ/M)$. Our numerical values are found to be in agreement with estimates first made within the Effective One Body formalism, and with predictions of the first law of black-hole-binary mechanics (as applied to the asymptotic circular orbit). Our calculation is based on a time-domain integration of the Lorenz-gauge perturbation equations, and it is a first such calculation for an unbound orbit. We tackle several technical difficulties specific to unbound orbits, illustrating how these may be handled in more general cases of unbound motion. Our method paves the way to calculations of the self-force along hyperbolic-type scattering orbits. Such orbits can probe the two-body potential down to the "light ring", and could thus supply strong-field calibration data for eccentricity-dependent terms in the Effective One Body model of merging binaries.

gr-qc↗