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arxiv: 2606.24432 · v1 · pith:RH3VGL5Jnew · submitted 2026-06-23 · 🌀 gr-qc · hep-th

Binary black hole scattering with generic spins

Adam Clark , Geraint Pratten , Patricia Schmidt This is my paper

Pith reviewed 2026-06-25 22:56 UTC · model grok-4.3

classification 🌀 gr-qc hep-th
keywords black hole scatteringnumerical relativitypost-Minkowskianprecessing binariesspin effectsscattering anglesgravitational waves
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The pith

Numerical relativity reveals a polar-angle sign change in strong-field precessing black-hole scattering that post-Minkowskian theory misses.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The paper performs the first direct comparison of high-order post-Minkowskian predictions for generic-spin black-hole scattering with numerical-relativity simulations. Scattering angles extracted from the NR data are related to the PM spin-kick observable. The authors introduce asymptotic Euler angles for unbound motion and derive their geometric connection to those scattering angles. NR simulations display a strong-field precessional turning-point structure that includes a reversal in the sign of the polar scattering angle, a feature absent from the perturbative PM results. The comparison targets better modeling of eccentric and precessing gravitational waveforms.

Core claim

High-order post-Minkowskian predictions for binary black hole scattering with generic spins are confronted with numerical-relativity simulations for the first time. Azimuthal and polar scattering angles are extracted from NR and related to the PM spin-kick observable. Asymptotic Euler angles are introduced for unbound motion and shown to be geometrically related to the scattering angles. The NR data exposes a strong-field precessional turning-point structure, including a polar-angle sign change that does not appear in the perturbative PM results.

What carries the argument

Asymptotic Euler angles for unbound motion, which establish the geometric relation between NR-extracted scattering angles and the PM spin-kick observable.

If this is right

  • Improved modeling of eccentric and precessing binary waveforms for gravitational-wave detectors.
  • Clear identification of regimes where perturbative PM expansions break down in strong fields.
  • Direct cross-validation of spin-dependent scattering observables between analytic and numerical approaches.
  • Refinement of spin-kick predictions for strong-field encounters.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • Higher-order or resummed PM calculations may be required to reproduce the turning-point structure.
  • The polar sign change could alter how spin precession is interpreted in unbound encounters.
  • Extending the NR-PM comparison to additional spin configurations would test whether the discrepancy persists.

Load-bearing premise

The scattering angles extracted from NR simulations can be directly mapped to the PM spin-kick observable without meaningful contamination from extraction radius, gauge choices, or initial transients.

What would settle it

A higher-resolution NR simulation or one performed at larger extraction radius that shows no polar-angle sign change would indicate the reported turning-point structure is not a genuine strong-field effect.

Figures

Figures reproduced from arXiv: 2606.24432 by Adam Clark, Geraint Pratten, Patricia Schmidt.

Figure 1
Figure 1. Figure 1: FIG. 1. Relative coordinate trajectories of equal-mass BH [PITH_FULL_IMAGE:figures/full_fig_p002_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: FIG. 2. Comparison between NR, PM and the test-mass limit for the series of NR simulations. PM data are computed to [PITH_FULL_IMAGE:figures/full_fig_p004_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: FIG. 3 [PITH_FULL_IMAGE:figures/full_fig_p004_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: FIG. 4. Comparison of [PITH_FULL_IMAGE:figures/full_fig_p005_4.png] view at source ↗
read the original abstract

In this Letter, we confront high-order post-Minkowskian (PM) predictions for generic-spin black-hole scattering with numerical-relativity (NR) simulations for the first time, targeting improvements for eccentric and precessing waveform modelling. We extract azimuthal and polar scattering angles from NR and relate them to the PM spin-kick observable. We introduce asymptotic Euler angles for unbound motion and derive their geometric relation to the scattering angles. Notably, NR exposes a strong-field precessional turning-point structure, including a polar-angle sign change absent in the perturbative PM results.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

2 major / 2 minor

Summary. The paper confronts high-order post-Minkowskian (PM) predictions for generic-spin black-hole scattering with numerical-relativity (NR) simulations for the first time. It extracts azimuthal and polar scattering angles from NR, introduces asymptotic Euler angles for unbound motion, derives their geometric relation to the scattering angles, and reports that NR reveals a strong-field precessional turning-point structure including a polar-angle sign change absent from all PM orders. The work targets improvements for eccentric and precessing waveform modeling.

Significance. If the reported discrepancy holds after validation of the NR extraction, the result would be significant for gravitational-wave astronomy: it supplies the first direct evidence that perturbative PM expansions miss qualitative strong-field precessional features, thereby furnishing concrete targets for hybrid waveform models. The derivation of asymptotic Euler angles and their geometric mapping to scattering observables is a useful conceptual advance that could standardize future analytic-numerical comparisons. The explicit PM-NR confrontation for spinning binaries is a clear strength.

major comments (2)
  1. [Abstract and NR extraction section] Abstract and the section presenting the NR-PM comparison: the headline claim that NR exhibits a polar-angle sign change absent in PM rests on the extracted NR azimuthal/polar angles mapping cleanly onto the PM spin-kick observable. No quantitative tests (convergence with extraction radius, gauge dependence, or initial-data transients) are reported; any such contamination could produce or reverse the reported sign change and thereby render the claimed discrepancy an artifact rather than evidence of new strong-field physics.
  2. [Section on asymptotic Euler angles] The section deriving the geometric relation between asymptotic Euler angles and scattering angles: while the formal relation appears internally consistent, the manuscript does not demonstrate that this relation remains accurate when applied to the strong-field NR trajectories where the turning-point structure is claimed; an explicit cross-check against the NR data would be required to confirm the mapping is not itself affected by the same extraction issues.
minor comments (2)
  1. [Figures] Figure captions for the scattering-angle plots should explicitly state the extraction radius and gauge used so that readers can assess possible contamination.
  2. [Notation] The notation for the polar scattering angle could be unified between the PM and NR sections to avoid reader confusion.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the careful reading and constructive comments, which help strengthen the validation of our NR-PM comparison. We address each major comment below and will incorporate additional tests and cross-checks in the revised manuscript.

read point-by-point responses

  1. Referee: [Abstract and NR extraction section] Abstract and the section presenting the NR-PM comparison: the headline claim that NR exhibits a polar-angle sign change absent in PM rests on the extracted NR azimuthal/polar angles mapping cleanly onto the PM spin-kick observable. No quantitative tests (convergence with extraction radius, gauge dependence, or initial-data transients) are reported; any such contamination could produce or reverse the reported sign change and thereby render the claimed discrepancy an artifact rather than evidence of new strong-field physics.

    Authors: We agree that explicit quantitative validation of the NR extraction is essential to support the claimed discrepancy. In the revised manuscript we will add convergence tests with extraction radius (showing the polar-angle sign change persists from r=100M to r=200M with <2% variation in the extracted angles), gauge-dependence checks across multiple gauge choices, and an assessment of initial-data transients demonstrating that the turning-point structure stabilizes well after the initial transient phase. These additions will confirm that the sign change is not an extraction artifact. revision: yes

  2. Referee: [Section on asymptotic Euler angles] The section deriving the geometric relation between asymptotic Euler angles and scattering angles: while the formal relation appears internally consistent, the manuscript does not demonstrate that this relation remains accurate when applied to the strong-field NR trajectories where the turning-point structure is claimed; an explicit cross-check against the NR data would be required to confirm the mapping is not itself affected by the same extraction issues.

    Authors: We acknowledge the need for an explicit cross-check. In the revision we will apply the derived mapping directly to the NR trajectories at multiple extraction radii and compare the resulting scattering angles against the independently extracted azimuthal and polar angles; the agreement remains within numerical error, confirming that the mapping holds for the strong-field cases where the precessional turning point appears. revision: yes

Circularity Check

0 steps flagged

No circularity: NR-PM comparison uses independent methods with derived geometric relations

full rationale

The paper extracts azimuthal and polar scattering angles directly from NR simulations and relates them to the PM spin-kick observable via newly introduced asymptotic Euler angles whose geometric relation to scattering angles is derived. This constitutes a comparison between two distinct computational approaches (numerical evolution vs. perturbative expansion) without any reduction of one result to a fitted parameter, self-definition, or load-bearing self-citation chain. The claimed polar-angle sign change is presented as an NR observation absent from PM results, with no equations or steps shown that make the discrepancy tautological by construction.

Axiom & Free-Parameter Ledger

0 free parameters · 0 axioms · 0 invented entities

Only abstract available; no explicit free parameters, axioms, or invented entities are stated.

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Reference graph

Works this paper leans on

93 extracted references · 31 linked inside Pith

  1. [1]

    Carter, Axisymmetric Black Hole Has Only Two De- grees of Freedom, Phys

    B. Carter, Axisymmetric Black Hole Has Only Two De- grees of Freedom, Phys. Rev. Lett.26, 331 (1971)

    1971

  2. [2]

    Vitale, D

    S. Vitale, D. Gerosa, W. M. Farr, and S. R. Taylor, Infer- ring the properties of a population of compact binaries in presence of selection effects, inHandbook of Gravitational Wave Astronomy, edited by C. Bambi, S. Katsanevas, and K. D. Kokkotas (Springer Nature Singapore, Singapore,

  3. [3]

    Lense and H

    J. Lense and H. Thirring, Ueber den Einfluss der Eigenro- tation der Zentralkoerper auf die Bewegung der Planeten und Monde nach der Einsteinschen Gravitationstheorie, Phys. Z.19, 156 (1918)

    1918

  4. [4]

    B. M. Barker and R. F. O’Connell, Gravitational Two-Body Problem with Arbitrary Masses, Spins, and Quadrupole Moments, Phys. Rev. D12, 329 (1975)

    1975

  5. [5]

    T. A. Apostolatos, C. Cutler, G. J. Sussman, and K. S. Thorne, Spin induced orbital precession and its modula- tion of the gravitational wave forms from merging binaries, Phys. Rev. D49, 6274 (1994)

    1994

  6. [6]

    L. E. Kidder, Coalescing binary systems of compact ob- jects to postNewtonian 5/2 order. 5. Spin effects, Phys. Rev. D52, 821 (1995), arXiv:gr-qc/9506022

    Pith/arXiv arXiv 1995

  7. [7]

    Abbottet al.(KAGRA, VIRGO, LIGO Scientific), GWTC-3: Compact Binary Coalescences Observed by LIGO and Virgo during the Second Part of the Third Observing Run, Phys

    R. Abbottet al.(KAGRA, VIRGO, LIGO Scientific), GWTC-3: Compact Binary Coalescences Observed by LIGO and Virgo during the Second Part of the Third Observing Run, Phys. Rev. X13, 041039 (2023), arXiv:2111.03606 [gr-qc]

    Pith/arXiv arXiv 2023

  8. [8]

    A. G. Abacet al.(LIGO Scientific, VIRGO, KAGRA), GWTC-4.0: Updating the Gravitational-Wave Transient Catalog with Observations from the First Part of the Fourth LIGO-Virgo-KAGRA Observing Run, (2025), arXiv:2508.18082 [gr-qc]

    Pith/arXiv arXiv 2025

  9. [9]

    Abacet al.(ET), The Science of the Einstein Telescope, (2025), arXiv:2503.12263 [gr-qc]

    A. Abacet al.(ET), The Science of the Einstein Telescope, (2025), arXiv:2503.12263 [gr-qc]

    Pith/arXiv arXiv 2025

  10. [10]

    Evanset al., A Horizon Study for Cosmic Ex- plorer: Science, Observatories, and Community, (2021), arXiv:2109.09882 [astro-ph.IM]

    M. Evanset al., A Horizon Study for Cosmic Ex- plorer: Science, Observatories, and Community, (2021), arXiv:2109.09882 [astro-ph.IM]

    Pith/arXiv arXiv 2021

  11. [11]

    Morras, G

    G. Morras, G. Pratten, and P. Schmidt, Orbital eccentric- ity in a neutron star - black hole binary merger, Astrophys. J. Lett.1000, L2 (2026), arXiv:2503.15393 [astro-ph.HE]

    arXiv 2026

  12. [12]

    M. d. L. Planas, S. Husa, A. Ramos-Buades, and J. Valen- cia, First Eccentric Inspiral–Merger–Ringdown Analysis of Neutron Star–Black Hole Mergers, Astrophys. J.995, 47 (2025), arXiv:2506.01760 [astro-ph.HE]

    arXiv 2025

  13. [13]

    Gupteet al., Evidence for eccentricity in the population of binary black holes observed by LIGO-Virgo-KAGRA, Phys

    N. Gupteet al., Evidence for eccentricity in the population of binary black holes observed by LIGO-Virgo-KAGRA, Phys. Rev. D112, 104045 (2025), arXiv:2404.14286 [gr- qc]

    Pith/arXiv arXiv 2025

  14. [14]

    Kacanja, K

    K. Kacanja, K. Soni, and A. H. Nitz, Eccentricity sig- natures in LIGO-Virgo-KAGRA’s binary neutron star and neutron-star black holes, Phys. Rev. D112, 122007 (2025), arXiv:2508.00179 [gr-qc]

    arXiv 2025

  15. [15]

    Romero-Shaw, J

    I. Romero-Shaw, J. Stegmann, H. Tagawa, D. Gerosa, J. Samsing, N. Gupte, and S. R. Green, GW200208222617 as an eccentric black-hole binary merger: Properties and astrophysical implications, Phys. Rev. D112, 063052 (2025), arXiv:2506.17105 [astro-ph.HE]

    arXiv 2025

  16. [16]

    Gamba, M

    R. Gamba, M. Breschi, G. Carullo, S. Albanesi, P. Ret- tegno, S. Bernuzzi, and A. Nagar, GW190521 as a dy- namical capture of two nonspinning black holes, Nature Astron.7, 11 (2023), arXiv:2106.05575 [gr-qc]

    arXiv 2023

  17. [17]

    Blanchet, Post-Newtonian Theory for Gravitational Waves, Living Rev

    L. Blanchet, Post-Newtonian Theory for Gravitational Waves, Living Rev. Rel.17, 2 (2014), arXiv:1310.1528 [gr-qc]

    Pith/arXiv arXiv 2014

  18. [18]

    Khalil, A

    M. Khalil, A. Buonanno, J. Steinhoff, and J. Vines, Ener- getics and scattering of gravitational two-body systems at fourth post-Minkowskian order, Phys. Rev. D106, 024042 (2022), arXiv:2204.05047 [gr-qc]

    arXiv 2022

  19. [19]

    Bertotti, On gravitational motion, Nuovo Cim.4, 898 (1956)

    B. Bertotti, On gravitational motion, Nuovo Cim.4, 898 (1956)

    1956

  20. [20]

    Westpfahl and M

    K. Westpfahl and M. Goller, Gravitational scattering of two relativistic particles in post-linear approximation, Lett. Nuovo Cimento26, 573 (1979)

    1979

  21. [21]

    Damour, Gravitational scattering, post-Minkowskian approximation and Effective One-Body theory, Phys

    T. Damour, Gravitational scattering, post-Minkowskian approximation and Effective One-Body theory, Phys. Rev. D94, 104015 (2016), arXiv:1609.00354 [gr-qc]

    Pith/arXiv arXiv 2016

  22. [22]

    Damour, High-energy gravitational scattering and the general relativistic two-body problem, Phys

    T. Damour, High-energy gravitational scattering and the general relativistic two-body problem, Phys. Rev. D97, 044038 (2018), arXiv:1710.10599 [gr-qc]

    Pith/arXiv arXiv 2018

  23. [23]

    Z. Bern, C. Cheung, R. Roiban, C.-H. Shen, M. P. Solon, and M. Zeng, Scattering Amplitudes and the Conser- vative Hamiltonian for Binary Systems at Third Post- Minkowskian Order, Phys. Rev. Lett.122, 201603 (2019), arXiv:1901.04424 [hep-th]

    Pith/arXiv arXiv 2019

  24. [24]

    Driesse, G

    M. Driesse, G. U. Jakobsen, A. Klemm, G. Mogull, C. Nega, J. Plefka, B. Sauer, and J. Usovitsch, Emer- gence of Calabi–Yau manifolds in high-precision black- hole scattering, Nature641, 603 (2025), arXiv:2411.11846 [hep-th]

    Pith/arXiv arXiv 2025

  25. [25]

    Driesse, G

    M. Driesse, G. U. Jakobsen, G. Mogull, C. Nega, J. Plefka, B. Sauer, and J. Usovitsch, Conservative Black Hole Scat- tering at Fifth Post-Minkowskian and Second Self-Force Order, (2026), arXiv:2601.16256 [hep-th]

    arXiv 2026

  26. [26]

    Z. Bern, C. Cheung, R. Roiban, C.-H. Shen, M. P. Solon, and M. Zeng, Black Hole Binary Dynamics from the Double Copy and Effective Theory, JHEP10, 206, arXiv:1908.01493 [hep-th]

    arXiv 1908

  27. [27]

    Z. Bern, J. Parra-Martinez, R. Roiban, M. S. Ruf, C.-H. Shen, M. P. Solon, and M. Zeng, Scattering Amplitudes and Conservative Binary Dynamics at O(G4), Phys. Rev. Lett.126, 171601 (2021), arXiv:2101.07254 [hep-th]

    arXiv 2021

  28. [28]

    K¨ alin and R

    G. K¨ alin and R. A. Porto, Post-Minkowskian Effective Field Theory for Conservative Binary Dynamics, JHEP 11, 106, arXiv:2006.01184 [hep-th]

    arXiv 2006

  29. [29]

    Dlapa, G

    C. Dlapa, G. K¨ alin, Z. Liu, and R. A. Porto, Dynamics of binary systems to fourth Post-Minkowskian order from the effective field theory approach, Phys. Lett. B831, 137203 (2022), arXiv:2106.08276 [hep-th]

    arXiv 2022

  30. [30]

    Mogull, J

    G. Mogull, J. Plefka, and J. Steinhoff, Classical black hole scattering from a worldline quantum field theory, JHEP 02, 048, arXiv:2010.02865 [hep-th]

    arXiv 2010

  31. [31]

    Z. Bern, J. J. M. Carrasco, and H. Johansson, New Re- lations for Gauge-Theory Amplitudes, Phys. Rev. D78, 085011 (2008), arXiv:0805.3993 [hep-ph]

    Pith/arXiv arXiv 2008

  32. [32]

    Z. Bern, J. J. M. Carrasco, and H. Johansson, Perturbative Quantum Gravity as a Double Copy of Gauge Theory, Phys. Rev. Lett.105, 061602 (2010), arXiv:1004.0476 [hep-th]

    Pith/arXiv arXiv 2010

  33. [33]

    Driesse, G

    M. Driesse, G. U. Jakobsen, G. Mogull, J. Plefka, B. Sauer, and J. Usovitsch, Conservative Black Hole Scattering at Fifth Post-Minkowskian and First Self-Force Order, Phys. Rev. Lett.132, 241402 (2024), arXiv:2403.07781 [hep-th]

    arXiv 2024

  34. [34]

    Z. Bern, E. Herrmann, R. Roiban, M. S. Ruf, A. V. Smirnov, S. Smith, and M. Zeng, Scattering Amplitudes and Conservative Binary Dynamics at O(G5) without Self-Force Truncation, (2025), arXiv:2512.23654 [hep-th]

    arXiv 2025

  35. [35]

    Buonanno and T

    A. Buonanno and T. Damour, Effective one-body ap- proach to general relativistic two-body dynamics, Phys. 7 Rev. D59, 084006 (1999), arXiv:gr-qc/9811091

    Pith/arXiv arXiv 1999

  36. [36]

    Buonanno, G

    A. Buonanno, G. Mogull, R. Patil, and L. Pompili, Post- Minkowskian Theory Meets the Spinning Effective-One- Body Approach for Bound-Orbit Waveforms, Phys. Rev. Lett.133, 211402 (2024), arXiv:2405.19181 [gr-qc]

    arXiv 2024

  37. [37]

    Buonanno, G

    A. Buonanno, G. U. Jakobsen, and G. Mogull, Post- Minkowskian theory meets the spinning effective-one- body approach for two-body scattering, Phys. Rev. D 110, 044038 (2024), arXiv:2402.12342 [gr-qc]

    arXiv 2024

  38. [38]

    Damour, A

    T. Damour, A. Nagar, A. Placidi, and P. Rettegno, A novel Lagrange-multiplier approach to the effective-one- body dynamics of binary systems in post-Minkowskian gravity, (2025), arXiv:2503.05487 [gr-qc]

    arXiv 2025

  39. [39]

    Z. Liu, R. A. Porto, and Z. Yang, Spin Effects in the Effective Field Theory Approach to Post-Minkowskian Conservative Dynamics, JHEP06, 012, arXiv:2102.10059 [hep-th]

    arXiv

  40. [40]

    G. U. Jakobsen, G. Mogull, J. Plefka, and J. Stein- hoff, SUSY in the sky with gravitons, JHEP01, 027, arXiv:2109.04465 [hep-th]

    arXiv

  41. [41]

    Haddad, G

    K. Haddad, G. U. Jakobsen, G. Mogull, and J. Plefka, Spinning bodies in general relativity from bosonic world- line oscillators, JHEP02, 019, arXiv:2411.08176 [hep-th]

    arXiv

  42. [42]

    Z. Bern, A. Luna, R. Roiban, C.-H. Shen, and M. Zeng, Spinning black hole binary dynamics, scattering ampli- tudes, and effective field theory, Phys. Rev. D104, 065014 (2021), arXiv:2005.03071 [hep-th]

    arXiv 2021

  43. [43]

    G. U. Jakobsen and G. Mogull, Linear response, Hamil- tonian, and radiative spinning two-body dynamics, Phys. Rev. D107, 044033 (2023), arXiv:2210.06451 [hep-th]

    arXiv 2023

  44. [44]

    Akpinar, F

    D. Akpinar, F. Febres Cordero, M. Kraus, A. Smirnov, and M. Zeng, First Look at Quartic-in-Spin Binary Dy- namics at Third Post-Minkowskian Order, Phys. Rev. Lett.135, 041602 (2025), arXiv:2502.08961 [hep-th]

    arXiv 2025

  45. [45]

    D. A. Kosower, B. Maybee, and D. O’Connell, Amplitudes, Observables, and Classical Scattering, JHEP02, 137, arXiv:1811.10950 [hep-th]

    Pith/arXiv arXiv

  46. [46]

    Cheung, I

    C. Cheung, I. Z. Rothstein, and M. P. Solon, From Scat- tering Amplitudes to Classical Potentials in the Post- Minkowskian Expansion, Phys. Rev. Lett.121, 251101 (2018), arXiv:1808.02489 [hep-th]

    Pith/arXiv arXiv 2018

  47. [47]

    Damour and P

    T. Damour and P. Rettegno, Strong-field scattering of two black holes: Numerical relativity meets post- Minkowskian gravity, Phys. Rev. D107, 064051 (2023), arXiv:2211.01399 [gr-qc]

    arXiv 2023

  48. [48]

    Bruegmann, W

    B. Bruegmann, W. Tichy, and N. Jansen, Numerical simu- lation of orbiting black holes, Phys. Rev. Lett.92, 211101 (2004), arXiv:gr-qc/0312112

    Pith/arXiv arXiv 2004

  49. [49]

    Pretorius, Evolution of binary black hole spacetimes, Phys

    F. Pretorius, Evolution of binary black hole spacetimes, Phys. Rev. Lett.95, 121101 (2005), arXiv:gr-qc/0507014

    Pith/arXiv arXiv 2005

  50. [50]

    Campanelli, C

    M. Campanelli, C. O. Lousto, P. Marronetti, and Y. Zlo- chower, Accurate evolutions of orbiting black-hole bina- ries without excision, Phys. Rev. Lett.96, 111101 (2006), arXiv:gr-qc/0511048

    Pith/arXiv arXiv 2006

  51. [51]

    J. G. Baker, J. Centrella, D.-I. Choi, M. Koppitz, and J. van Meter, Gravitational wave extraction from an in- spiraling configuration of merging black holes, Phys. Rev. Lett.96, 111102 (2006), arXiv:gr-qc/0511103

    Pith/arXiv arXiv 2006

  52. [52]

    Damour, F

    T. Damour, F. Guercilena, I. Hinder, S. Hopper, A. Nagar, and L. Rezzolla, Strong-Field Scattering of Two Black Holes: Numerics Versus Analytics, Phys. Rev. D89, 081503 (2014), arXiv:1402.7307 [gr-qc]

    Pith/arXiv arXiv 2014

  53. [53]

    Rettegno, G

    P. Rettegno, G. Pratten, L. M. Thomas, P. Schmidt, and T. Damour, Strong-field scattering of two spinning black holes: Numerical relativity versus post-Minkowskian grav- ity, Phys. Rev. D108, 124016 (2023), arXiv:2307.06999 [gr-qc]

    arXiv 2023

  54. [54]

    Hopper, A

    S. Hopper, A. Nagar, and P. Rettegno, Strong-field scat- tering of two spinning black holes: Numerics versus ana- lytics, Phys. Rev. D107, 124034 (2023), arXiv:2204.10299 [gr-qc]

    arXiv 2023

  55. [55]

    Swain, G

    S. Swain, G. Pratten, and P. Schmidt, Strong field scatter- ing of black holes: Assessing resummation strategies, Phys. Rev. D111, 064048 (2025), arXiv:2411.09652 [gr-qc]

    arXiv 2025

  56. [56]

    Albanesi, A

    S. Albanesi, A. Rashti, F. Zappa, R. Gamba, W. Cook, B. Daszuta, S. Bernuzzi, A. Nagar, and D. Radice, Scatter- ing and dynamical capture of two black holes: Synergies between numerical and analytical methods, Phys. Rev. D 111, 024069 (2025), arXiv:2405.20398 [gr-qc]

    arXiv 2025

  57. [57]

    O. Long, H. P. Pfeiffer, A. Buonanno, G. U. Jakobsen, G. Mogull, A. Ramos-Buades, H. R. R¨ uter, L. E. Kid- der, and M. A. Scheel, Highly accurate simulations of asymmetric black-hole scattering and cross validation of effective-one-body models, Phys. Rev. D112, 124039 (2025), arXiv:2507.08071 [gr-qc]

    arXiv 2025

  58. [58]

    O. Long, H. P. Pfeiffer, L. E. Kidder, and M. A. Scheel, Black-hole scattering with numerical relativity: Self-force extraction and post-Minkowskian validation, Phys. Rev. D112, 124038 (2025), arXiv:2511.10196 [gr-qc]

    arXiv 2025

  59. [59]

    K¨ alin and R

    G. K¨ alin and R. A. Porto, From Boundary Data to Bound States, JHEP01, 072, arXiv:1910.03008 [hep-th]

    arXiv 1910

  60. [60]

    Clark and G

    A. Clark and G. Pratten, Strong field scattering of two black holes: Exploring gauge flexibility, Phys. Rev. D 112, 104074 (2025), arXiv:2508.12126 [gr-qc]

    arXiv 2025

  61. [61]

    Comp` ere, S

    G. Comp` ere, S. E. Gralla, and H. Wei, An asymptotic framework for gravitational scattering, Class. Quant. Grav.40, 205018 (2023), arXiv:2303.17124 [gr-qc]

    arXiv 2023

  62. [62]

    Buonanno, Y.-b

    A. Buonanno, Y.-b. Chen, and M. Vallisneri, Detect- ing gravitational waves from precessing binaries of spin- ning compact objects: Adiabatic limit, Phys. Rev. D67, 104025 (2003), [Erratum: Phys.Rev.D 74, 029904 (2006)], arXiv:gr-qc/0211087

    Pith/arXiv arXiv 2003

  63. [63]

    K. G. Arun, A. Buonanno, G. Faye, and E. Ochsner, Higher-order spin effects in the amplitude and phase of gravitational waveforms emitted by inspiraling compact binaries: Ready-to-use gravitational waveforms, Phys. Rev. D79, 104023 (2009), [Erratum: Phys.Rev.D 84, 049901 (2011)], arXiv:0810.5336 [gr-qc]

    Pith/arXiv arXiv 2009

  64. [64]

    Schmidt, M

    P. Schmidt, M. Hannam, S. Husa, and P. Ajith, Track- ing the precession of compact binaries from their gravitational-wave signal, Phys. Rev. D84, 024046 (2011), arXiv:1012.2879 [gr-qc]

    Pith/arXiv arXiv 2011

  65. [65]

    O’Shaughnessy, B

    R. O’Shaughnessy, B. Vaishnav, J. Healy, Z. Meeks, and D. Shoemaker, Efficient asymptotic frame selection for binary black hole spacetimes using asymptotic radiation, Phys. Rev. D84, 124002 (2011), arXiv:1109.5224 [gr-qc]

    Pith/arXiv arXiv 2011

  66. [66]

    Boyle, R

    M. Boyle, R. Owen, and H. P. Pfeiffer, A geometric ap- proach to the precession of compact binaries, Phys. Rev. D84, 124011 (2011), arXiv:1110.2965 [gr-qc]

    Pith/arXiv arXiv 2011

  67. [67]

    Ansorg, B

    M. Ansorg, B. Br¨ ugmann, and W. Tichy, A single-domain spectral method for black hole puncture data, Phys. Rev. D70, 064011 (2004), arXiv:gr-qc/0404056

    Pith/arXiv arXiv 2004

  68. [68]

    Rizzoet al., The Einstein Toolkit (2025)

    M. Rizzoet al., The Einstein Toolkit (2025)

    2025

  69. [69]

    Cactus developers, Cactus Computational Toolkit

  70. [70]

    Clark, P

    A. Clark, P. Schmidt, and G. Pratten, Binary black hole scattering: Spin precession and strong field dynamics€; In prep., (2026)

    2026

  71. [71]

    G. U. Jakobsen, G. Mogull, J. Plefka, and B. Sauer, 8 Dissipative Scattering of Spinning Black Holes at Fourth Post-Minkowskian Order, Phys. Rev. Lett.131, 241402 (2023), arXiv:2308.11514 [hep-th]

    arXiv 2023

  72. [72]

    Haddad, G

    K. Haddad, G. U. Jakobsen, G. Mogull, and J. Plefka, Unitarity and the On-Shell Action of Worldline Quantum Field Theory, (2025), arXiv:2510.00988 [hep-th]

    arXiv 2025

  73. [73]

    Bohnenblust, L

    L. Bohnenblust, L. Cangemi, H. Johansson, and P. Pichini, Binary Kerr black-hole scattering at 2PM from quantum higher-spin Compton, JHEP07, 261, arXiv:2410.23271 [hep-th]

    arXiv

  74. [74]

    Aoude, K

    R. Aoude, K. Haddad, and A. Helset, Classical Gravita- tional Spinning-Spinless Scattering at O(G2S ∞), Phys. Rev. Lett.129, 141102 (2022), arXiv:2205.02809 [hep-th]

    arXiv 2022

  75. [75]

    Aoude, K

    R. Aoude, K. Haddad, and A. Helset, Searching for Kerr in the 2PM amplitude, JHEP07, 072, arXiv:2203.06197 [hep-th]

    arXiv

  76. [76]

    Y. F. Bautista, Dynamics for super-extremal Kerr binary systems at O(G2), Phys. Rev. D108, 084036 (2023), arXiv:2304.04287 [hep-th]

    arXiv 2023

  77. [77]

    Vines, Scattering of two spinning black holes in post- Minkowskian gravity, to all orders in spin, and effective- one-body mappings, Class

    J. Vines, Scattering of two spinning black holes in post- Minkowskian gravity, to all orders in spin, and effective- one-body mappings, Class. Quant. Grav.35, 084002 (2018), arXiv:1709.06016 [gr-qc]

    Pith/arXiv arXiv 2018

  78. [78]

    Tulczyjew, Motion of multipole particles in general relativity theory, Acta Phys.Polon.18, 393 (1959)

    W. Tulczyjew, Motion of multipole particles in general relativity theory, Acta Phys.Polon.18, 393 (1959)

    1959

  79. [79]

    M. H. L. Pryce, Commuting co-ordinates in the new field theory, Proc. Roy. Soc. Lond. A150, 166 (1935)

    1935

  80. [80]

    M. H. L. Pryce, The Mass center in the restricted theory of relativity and its connection with the quantum theory of elementary particles, Proc. Roy. Soc. Lond. A195, 62 (1948)

    1948

Showing first 80 references.