arXiv subjects

Adam Pound

Publications and source records attributed to Adam Pound.

At least 19 recordsLinked to original sources

arXiv2026

Point particles in general relativity: beyond linear perturbation theory

Point particles are generically ill defined in fully nonlinear general relativity, although they are naturally well defined in linear perturbation theory. In a previous paper, two of us showed how they can be rigorously defined from matched asymptotic expansions at second order in perturbation theory on a generic background spacetime. Here we show how the resulting field equations can be recast in a more practical, more fully ``skeletonized'' form. We also show that this form of the field equations enables simple derivations of equations of motion. Finally, we show how calculations in second-order perturbation theory can bypass the use of singular ``punctures'' and make rigorous use of off-the-shelf regularization methods such as Hadamard regularization, opening new avenues to second-order self-force calculations in black hole binaries.

gr-qc↗

arXiv2026

Second-order Teukolsky calculations for nonspinning, quasicircular binaries

Currently, the only second-order gravitational self-force calculations have been based on directly solving the perturbative Einstein equations in the Lorenz gauge. That method relied on the complete separability of the Einstein equations in a Schwarzschild background. In this paper, we present a new scheme based on the second-order Teukolsky equation. Crucially, this method promises to extend (reasonably straightforwardly) to the more realistic case of a Kerr background. Here we implement the scheme in the simplest setting of quasicircular orbits around a Schwarzschild black hole. In addition to working with the Teukolsky equation, our scheme incorporates several other advances over previous second-order self-force calculations: compactified hyperboloidal slicing, transformation to a Bondi-Sachs gauge, and a combination of spectral and variation-of-parameters methods. We also use these tools to re-examine the infrared divergences that arise in second-order Lorenz-gauge calculations, showing they are less pronounced in the Teukolsky case and completely eliminated in the Bondi-Sachs gauge. We conclude by calculating the asymptotic energy fluxes and benchmarking them against previous Lorenz-gauge calculations.

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arXiv2026

Dissection of a merger-ringdown waveform in the small-mass-ratio limit

Work over the past two decades has unveiled the rich phenomenology of black hole binary mergers and subsequent ringdowns, involving a tapestry of quasinormal modes (QNMs), nonlinearities, tails, transients, and secular effects including gravitational memory. Here we develop a framework for analyzing nonlinear merger-ringdown features in the small-mass-ratio limit, where individual effects can be cleanly isolated. Specializing to the case of a quasicircular, nonspinning black hole binary, we find the waveform sharply divides into a pre-merger extended inspiral phase, a merger phase lasting roughly half a cycle, and a post-merger ringdown dominated by QNMs. We show quadratic QNMs dominate over linear overtones in the ringdown phase for comparable-to-intermediate mass ratios, and we highlight nonlinear effects of gravitational-wave memory, including cubic wave-zone phenomena analogous to horizon absorption effects.

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arXiv2026

Quadrupole and quadratic-in-spin effects in quasicircular, spinning, asymmetric binaries

Next-generation gravitational-wave detectors will require significant improvements in current theoretical waveform models, particularly in the case of asymmetric-mass binaries. Here we provide one such improvement by calculating fully relativistic finite-size effects for small mass ratios -- primarily, fluxes of energy -- including quadratic-in-secondary-spin terms, spin-induced quadrupole terms, and tidally induced quadrupole terms, for quasicircular inspirals of a small companion into a Kerr black hole. We formulate these calculations within a multiscale waveform-generation framework in self-force theory, which could be used, with an energy-balance law we derive, to develop self-contained waveform models for asymmetric binaries involving stars orbiting black holes. Our results could additionally be used to improve other families of waveform models across all mass ratios. We present results both as complete numerical data sets on a Chebyshev grid and as analytical post-Newtonian expansions (to sixth PN order relative to the leading term in each contribution to the flux).

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arXiv2026

The Bondi--Sachs gauge, BMS frames, and memory in black hole perturbation theory

As LISA and other next-generation detectors demand increasingly accurate waveform models, there is a growing need for these models to precisely control gauge freedoms that had previously been inconsequential. One such intrinsic freedom is the choice of the asymptotic Bondi--Metzner--Sachs (BMS) frame. The need to control the BMS frame is particularly pronounced in black hole perturbation theory, where there has been little work to this end -- most glaringly in gravitational self-force calculations, which are in an unknown frame and encounter infrared, far-zone gauge singularities at second perturbative order. Here we present a framework for iteratively transforming to the Bondi--Sachs gauge and fixing the BMS frame on a Kerr background. This includes an extension of the Bondi--Sachs formalism to the multiscale expansions that underpin most self-force-based waveforms, introducing soft hair and a concept of ``forgetful gauges'' in the process. Our framework evades infrared divergences and naturally incorporates memory effects that had previously only ever been added ``after the fact'' in self-force waveforms, including the recently discovered ``memory distortion''. Our formalism could also be used for ringdown analysis, and we expect it to be vital for comparisons with numerical relativity and post-Newtonian theory.

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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

Constants of motion in gravitational self-force theory

Synergies between self-force theory and other approaches to the gravitational two-body problem have traditionally relied on calculations of gauge-invariant observables as functions of orbital frequencies. However, in self-force theory, one can also define a complete set of constants of motion: energy, azimuthal angular momentum, and radial and polar actions. Here, we outline how directly utilizing these constants allows for more straightforward comparisons and hybridizations across the parameter space, as well as more streamlined waveform generation through flux-balance laws. Restricting to the case of nonspinning binaries and first order in self-force, we compute the constants of motion and the corrections to fundamental frequencies numerically as well as analytically (to 9PN in a post-Newtonian expansion), establishing consistency with the highest-order (4PN) results available from post-Newtonian theory. We also apply the results to identify the perturbed locations of special curves in the parameter space: circular orbits and the separatrix between bound and plunging orbits.

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arXiv2025

Spin-aligned inspiral waveforms from self-force and post-Newtonian theory

We present the state-of-the-art waveform model WaSABI-C for quasicircular inspirals of spinning black hole binaries with aligned or anti-aligned spins. Our model synthesizes the most up-to-date first- and second-order gravitational self-force results with high-order post-Newtonian expansions through a systematic hybridization procedure. This approach captures both strong-field and weak-field dynamics with high fidelity, enabling accurate modeling of spin-(anti)aligned inspirals across a wide parameter space. The resulting waveforms mark a significant advance in the precision of self-force-based templates, providing critical input for the detection and interpretation of gravitational waves from compact binaries with future observatories such as LISA and ET. We accompany this work with the release of WaSABI (Waveform Simulations of Asymmetric Binary Inspirals), a public package implementing our model for community use and further development.

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arXiv2025

Hybrid waveform model for asymmetric spinning binaries: Self-force meets post-Newtonian theory

We develop and implement a new hybrid waveform model for quasicircular inspirals with a spinning primary and nonspinning secondary, excluding the merger and ringdown. This model, which is a core component of the more extensive WaSABI-C model, consistently assembles all available first-order self-force and post-Newtonian results through a hybridization procedure without any tuning to numerical relativity, making it particularly suited for intermediate to extreme mass ratios. For almost all masses and primary spins, the resulting hybrid model significantly improves the faithfulness of both post-Newtonian and adiabatic self-force waveforms considered separately. We provide detailed comparisons with 50 simulations from the SXS catalog with mass ratios ranging from 1 to 15 and primary spins ranging from -0.8 to 0.8. The hybrid model improves the median mismatch against numerical relativity waveforms by a factor of 2000 with respect to adiabatic waveforms and 40 with respect to post-Newtonian waveforms. The mismatches are comparable to those obtained from the SEOBNRv5EHM model in the quasicircular limit over most of the parameter space covered by NR simulations.

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arXiv2025

Post-adiabatic self-force waveforms: slowly spinning primary and precessing secondary

Recent progress in gravitational self-force theory has led to the development of a first post-adiabatic (1PA) waveform model for nonspinning, quasicircular compact binaries [Phys. Rev. Lett. 130, 241402 (2023)]. In this paper, we extend that model to allow for a slowly spinning primary black hole and a generic, precessing spin on the secondary object, restricting to the case of small misalignment between the primary spin and the orbital angular momentum. We demonstrate excellent agreement between our waveforms and fully nonlinear numerical relativity simulations for mass ratios $q\gtrsim 5$ and primary spins $|\chi_1|\lesssim 0.1$ and arbitrary secondary spin $\chi_2 \lesssim 1$. In particular we present the re-summed 1PAT1R waveform model, which significantly improves the accuracy of the original 1PAT1 waveforms for comparable masses and increasing primary spin. Our models are publicly available in the WaSABI package.

gr-qc↗

arXiv2025

Transition-to-plunge self-force waveforms with a spinning primary

With the upcoming third-generation gravitational-wave detectors comes the need to build complete, faithful, and fast waveform models for asymmetric-mass-ratio compact binaries. Most efforts within the self-force community have focused on modeling these binaries' inspiral regime, but for ground-based detectors the systems' final merger can represent the dominant part of the signal. Recent work by three of us has extended the multiscale self-force framework through the transition-to-plunge and merger-ringdown regimes for nonspinning binaries. In this paper, we generalize the next-to-next-to-leading-order transition-to-plunge waveform model to include the spin of the primary black hole. We also improve the construction of composite inspiral-transition waveform models by performing a change of variables on the binary's mechanical phase space during the transition to plunge. We provide detailed discussions of our numerical implementation and comparisons with numerical relativity simulations.

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arXiv2025

Black hole mergers beyond general relativity: a self-force approach

Gravitational waves from binary black hole mergers provide a glimpse of gravitational dynamics in its most extreme observable regime, potentially enabling precision tests of general relativity (GR) and of the Kerr description of black holes. However, until recently, numerical simulations of black hole mergers have not been possible in theories beyond GR. While recent breakthroughs have overcome that obstacle, simulations covering the full, interesting range of binary parameters remain unfeasible. Here we present a new first-principles approach to this problem. We show how self-force theory can be used to model the merger and ringdown of black holes in a broad class of gravitational theories, assuming one object is much smaller than the other. We calculate self-force effects on the merger waveform for the first time, and we demonstrate how our formulation allows us to modularly compute beyond-GR effects and readily incorporate them into a fast merger-ringdown waveform model.

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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↗

arXiv2025

Post-adiabatic dynamics and waveform generation in self-force theory: an invariant pseudo-Hamiltonian framework

Gravitational waveform modeling in self-force theory has reached a mature stage in recent years, with fast and accurate models emerging at both adiabatic (0PA) and first post-adiabatic (1PA) orders in a multiscale expansion. Here, we provide a gauge-invariant 1PA waveform-generation framework that involves no direct calculation of the (gauge-dependent) self-force. To achieve this, we recast the multiscale framework in a pseudo-Hamiltonian form, working on the six-dimensional phase space intrinsic to the multiscale expansion. We characterize the gauge freedom on phase space and show how a localization procedure avoids nonlocal-in time effects in the 1PA dynamics. We find a conservative Hamiltonian structure can be naturally embedded into the complete, dissipative 1PA pseudo-Hamiltonian dynamics, giving rise to natural definitions of the conserved energy, angular momentum, and radial and polar actions. As a byproduct, we clarify that the on-shell value of the conservative Hamiltonian is equal to the mechanical energy historically predicted by the first law of binary black hole mechanics.

gr-qc↗

arXiv2025

Self-force framework for merger-ringdown waveforms

The prospect of observing asymmetric compact binaries with next-generation gravitational-wave detectors has motivated the development of fast and accurate waveform models in gravitational self-force theory. These models are based on a two-stage process: in a (slow) offline stage, waveform ingredients are pre-computed as functions on the orbital phase space; in a (fast) online stage, the waveform is generated by evolving through the phase space. While this framework has traditionally been restricted to the inspiral stage of a binary, we recently extended it across the transition to plunge, where the small companion crosses the innermost stable circular orbit around the primary black hole. In this paper, for the special case of quasicircular, nonspinning binaries, we show how the "offline/online" phase-space paradigm also extends through the final plunge, which generates the binary's merger-ringdown signal. We implement the method at leading, geodesic order in the plunge. The resulting plunge waveform agrees well with a stationary-phase approximation at early times and with a (self-consistently calculated) quasinormal mode sum at late times, but we highlight that neither of the two approximations reaches the peak of the full plunge waveform. Finally, we compare the plunge waveform to numerical relativity simulations. Our framework offers the prospect of fast, accurate inspiral-merger-ringdown waveform models for asymmetric binaries.

gr-qc↗

arXiv2025

Quadratic quasinormal modes at null infinity on a Schwarzschild spacetime

The ringdown of perturbed black holes has been studied since the 1970s, but until recently, studies have focused on linear perturbations. There is now burgeoning interest in nonlinear perturbative effects during ringdown. Here, using a hyperboloidal framework, we provide a complete treatment of linear and quadratic quasinormal modes (QNMs and QQNMs) in second-order perturbation theory, in Schwarzschild spacetime. We include novel methods for extracting QNMs and QQNMs amplitudes using a Laplace transform treatment, allowing for the inclusion of arbitrary initial data. We produce both time- and frequency-domain codes. From these codes, we present new results further exploring the unforeseen dependence of QQNMs amplitudes on the parity of the progenitor system, as demonstrated in our letter [Phys. Rev. Lett. 134, 061401 (2025)]. Our numerical results are restricted to perturbations of a Schwarzschild black hole, but our methods extend straightforwardly to the astrophysically realistic case of a Kerr black hole.

gr-qc↗

arXiv2025

Post-adiabatic waveform-generation framework for asymmetric precessing binaries

Recent years have seen rapid progress in calculations of gravitational waveforms from asymmetric compact binaries containing spinning secondaries. Here we outline a complete waveform-generation scheme, through first post-adiabatic order (1PA) in gravitational self-force theory, for generic secondary spin and generic (eccentric, precessing) orbital configurations around a generic Kerr primary. We emphasize the utility of a Fermi-Walker frame in parametrizing the secondary spin, and we analyse precession and nutation effects in the spin-orbit dynamics. We also explain convenient gauge choices within the waveform-generation scheme, and the gauge invariance of the resulting waveform. Finally, we highlight that, thanks to recent results due to Grant and Witzany et al., all relevant spin effects at 1PA order can now be computed without evaluating local self-forces or torques.

gr-qc↗

arXiv2024

Gravitational memory: new results from post-Newtonian and self-force theory

We compute the (displacement) gravitational wave memory due to a quasicircular inspiral of two black holes using a variety of perturbative techniques. Within post-Newtonian theory, we extend previous results for non-spinning binaries to 3.5PN order. Using the gravitational self-force approach, we compute the memory at first order in the mass ratio for inspirals into a Kerr black hole. We do this both numerically and via a double post-Newtonian--self-force expansion which we carry out to 5PN order. At second order in the self-force approach, near-zone calculations encounter an infrared divergence associated with memory, which is resolved through matching the near-zone solution to a post-Minkowskian expansion in the far zone. We describe that matching procedure for the first time and show how it introduces nonlocal-in-time memory effects into the two-body dynamics at second order in the mass ratio, as was also predicted by recent 5PN calculations within the effective field theory approach. We then compute the gravitational-wave memory through second order in the mass ratio (excluding certain possible memory distortion effects) and find that it agrees well with recent results from numerical relativity simulations for near-comparable-mass binaries.

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