arXiv subjects

Benjamin Leather

Publications and source records attributed to Benjamin Leather.

12 recordsLinked to original sources

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

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.

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arXiv2025

Inspiral-merger-ringdown waveforms with gravitational self-force results within the effective-one-body formalism

Gravitational self-force (GSF) theory is a strong-gravity perturbative approach to the relativistic two-body problem, primarily developed to model extreme-mass-ratio inspirals, where one compact object is significantly more massive than the companion. However, recent advancements in GSF calculations, particularly involving second-order self-force (2GSF) results, indicated a much broader applicability across a wider range of mass ratios. These developments have motivated efforts to incorporate GSF results into the effective-one-body (EOB) framework, where they have already been successfully integrated into the state-of-the-art waveform model, SEOBNRv5, employed in recent LIGO-Virgo-KAGRA (LVK) observing runs. In this work, we present SEOBNR-GSF, a nonspinning inspiral-merger-ringdown (IMR) EOB waveform model that introduces a GSF-informed EOB Hamiltonian as its central innovation. This marks the first complete IMR waveform model constructed primarily from GSF results. We show that our model outperforms inspiral waveforms from full 2GSF calculations in the intermediate-to-comparable mass regime. Furthermore, by comparing with a post-Newtonian-informed variant, SEOBNR-GSF-PN, we demonstrate that the inclusion of numerical GSF information in the Hamiltonian leads to significant improvements in model fidelity. Finally, we benchmark our model against high-accuracy, nonspinning numerical-relativity simulations from the Simulating eXtreme Spacetimes (SXS) catalogue and find that its median mismatch is comparable to that of SEOBNRv5, suggesting that this approach holds promise for further enhancing future EOB waveform models.

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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.

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arXiv2024

Gravitational self-force with hyperboloidal slicing and spectral methods

We present a novel approach for calculating the gravitational self-force (GSF) in the Lorenz gauge, employing hyperboloidal slicing and spectral methods. Our method builds on the previous work that applied hyperboloidal surfaces and spectral approaches to scalar-field toy model [Phys. Rev. D 105, 104033 (2022)], extending them to handle gravitational perturbations. Focusing on first-order metric perturbations, we address the construction of the hyperboloidal foliation, detailing the minimal gauge choice. The Lorenz gauge is adopted to facilitate well-understood regularisation procedures, which are essential for obtaining physically meaningful GSF results. We calculate of the Lorenz gauge metric perturbation via a (known) gauge transformation from the Regge-Wheeler gauge. Our approach yields a robust framework for obtaining the metric perturbation components needed to calculate key physical quantities, such as radiative fluxes, the Detweiler redshift, and self-force corrections. Furthermore, the compactified hyperboloidal approach allows us to efficiently calculate the metric perturbation throughout the entire spacetime. This work thus establishes a foundational methodology for future second-order GSF calculations within this gauge, offering computational efficiencies through spectral methods.

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arXiv2024

Quadratic quasi-normal mode dependence on linear mode parity

Quasinormal modes (QNMs) uniquely describe the dominant piece of the gravitational-wave ringdown of postmerger black holes. While the linear QNM regime has been extensively studied, recent work has highlighted the importance of second-perturbative-order, quadratic QNMs (QQNMs) arising from the nonlinear coupling of linear QNMs. Previous attempts to quantify the magnitude of these QQNMs have shown discrepant results. Using a new hyperboloidal framework, we resolve the discrepancy by showing that the QQNM/QNM ratio is a function not only of the black hole parameters but also of the ratio between even- and odd-parity linear QNMs: the ratio QQNM/QNM depends on what created the ringing black hole, but only through this ratio of even- to odd-parity linear perturbations.

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arXiv2024

Implementation of a GHZ-Teukolsky puncture scheme for gravitational self-force calculations

Post-adiabatic models of extreme- and intermediate-mass-ratio inspirals will require calculations of second-order gravitational self-force effects in the spacetime of a spinning, Kerr black hole. We take a step toward such calculations by implementing the recently formulated Teukolsky puncture scheme with Green-Hollands-Zimmerman metric reconstruction [CQG 39, 015019 (2022)]. This scheme eliminates the critical obstacle of gauge singularities that arise in the standard no-string metric reconstruction. Our first proof-of-principle implementation is limited to the simple case of circular orbits in Schwarzschild spacetime, but the method also applies to generic orbits on a Kerr background. We conclude with a discussion of various approaches to the second-order self-force problem in Kerr.

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arXiv2023

Worldtube puncture scheme for first- and second-order self-force calculations in the Fourier domain

Second-order gravitational self-force theory has recently led to the breakthrough calculation of ``first post-adiabatic'' (1PA) compact-binary waveforms [Phys. Rev. Lett. 130, 241402 (2023)]. The computations underlying those waveforms depend on a method of solving the perturbative second-order Einstein equation on a Schwarzschild background in the Fourier domain. In this paper we present that method, which involves dividing the domain into several regions. Different regions utilize different time slicings and allow for the use of ``punctures'' to tame sources and enforce physical boundary conditions. We demonstrate the method for Lorenz-gauge and Teukolsky equations in the relatively simple case of calculating parametric derivatives (``slow time derivatives'') of first-order fields, which are an essential input at second order.

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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.

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arXiv2023

Applying the effective-source approach to frequency-domain self-force calculations for eccentric orbits

Extreme mass-ratio inspirals (EMRIs) are expected to have considerable eccentricity when emitting gravitational waves (GWs) in the LISA band. Developing GW templates that remain phase accurate over these long inspirals requires the use of second-order self-force theory and practical second-order self-force calculations are now emerging for quasi-circular EMRIs. These calculations rely on effective-source regularization techniques in the frequency domain that presently are specialized to circular orbits. Here we make a first step towards more generic second-order calculations by extending the frequency domain effective-source approach to eccentric orbits. In order to overcome the slow convergence of the Fourier sum over radial modes, we develop a new extended effective-sources approach which builds upon the method of extended particular solutions. To demonstrate our new computational technique we apply it a toy scalar-field problem which is conceptually similar to the gravitational case.

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arXiv2022

Hyperboloidal method for frequency-domain self-force calculations

Gravitational self-force theory is the leading approach for modeling gravitational wave emission from small mass-ratio compact binaries. This method perturbatively expands the metric of the binary in powers of the mass ratio. The source for the perturbations depends on the orbital configuration, calculational approach, and the order of the perturbative expansion. These sources fall into three broad classes: (i) distributional, (ii) worldtube, and (iii) unbounded support. The latter, in particular, is important for emerging second-order (in the mass ratio) calculations. Traditional frequency domain approaches employ the variation of parameters method and compute the perturbation on standard time slices with numerical boundary conditions supplied at finite radius from series expansions of the asymptotic behavior. This approach has been very successful, but the boundary conditions calculations are tedious, and the approach is not well suited to unbounded sources where homogeneous solutions must be computed at all radii. This work develops an alternative approach where hyperboloidal slices foliate the spacetime, and compactifying coordinates simplify the boundary treatment. We implement this approach with a multi-domain spectral solver with analytic mesh refinement and use the scalar-field self-force on circular orbits around a Schwarzschild black hole as an example problem. The method works efficiently for all three source classes encountered in self-force calculations and has distinct advantages over the traditional approach. For example, our code efficiently computes the perturbation for orbits with extremely large orbital radii ($r_{p}>10^5M$) or modes with very high spherical harmonic mode index ($\ell \ge 100$). Our results indicate that hyperboloidal methods can play an essential role in self-force calculations.

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