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arxiv: 2606.11423 · v1 · pith:BFIB6P4Mnew · submitted 2026-06-09 · ✦ hep-th · gr-qc

Weak-field waveforms for generic relativistic orbits

Stefano De Angelis This is my paper

Pith reviewed 2026-06-27 12:04 UTC · model grok-4.3

classification ✦ hep-th gr-qc
keywords worldline formalismgravitational waveformsSchwinger-Keldysh path integralweak-field expansionEinstein equationsrelativistic orbitsintegro-differential equationspost-Minkowskian
0
0 comments X

The pith

Einstein's equations recast as integro-differential equations for worldlines by integrating out gravity.

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

This paper shows how the Schwinger-Keldysh path integral integrates out the gravitational field from Einstein's equations to produce ordinary integro-differential equations for the worldlines of bodies. Solutions to these equations can be obtained for generic relativistic orbits in the weak-field expansion. An independent calculation then produces the gravitational waveform for unspecified orbits, so the worldline solutions are inserted directly into the waveform expression. The two steps require no map between scattering and bound-orbit observables and avoid integration-by-parts identities. The framework is developed explicitly at leading and next-to-leading order.

Core claim

By applying the Schwinger-Keldysh path integral to Einstein's equations the gravitational field is integrated out, yielding classical integro-differential equations of motion for worldlines. These equations are solved for generic orbits and the solutions are inserted into a separately derived waveform formula. The derivation needs no scattering-to-bound map and automatically incorporates retardation and radiation effects without mode separation.

What carries the argument

Schwinger-Keldysh path integral that integrates out the gravitational field to produce integro-differential worldline equations whose solutions are inserted into an independent waveform expression.

If this is right

  • Equations of motion can be used directly inside an Effective One-Body framework because retardation and radiation are included automatically.
  • No separation of potential and radiation modes is required.
  • The waveform computation supplies an alternative route to Effective One-Body results when combined with suitable resummation.
  • All computations at leading and next-to-leading order bypass integration-by-parts identities.

Where Pith is reading between the lines

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

  • The modular separation of motion and waveform steps may allow hybrid calculations that combine this method with other perturbative expansions for binary systems.
  • Higher-order extensions of the weak-field strategy could be checked against existing post-Newtonian or post-Minkowskian benchmarks for specific orbits.
  • The approach suggests a route to waveform templates for generic orbits that does not presuppose a bound-orbit or scattering reduction.

Load-bearing premise

The Schwinger-Keldysh path integral applied to Einstein's equations produces classical integro-differential worldline equations that can be inserted into a waveform formula without extra consistency conditions.

What would settle it

A explicit computation of the waveform at next-to-leading order for a chosen weak-field orbit using the derived equations that disagrees with the standard post-Minkowskian result would falsify the framework.

Figures

Figures reproduced from arXiv: 2606.11423 by Stefano De Angelis.

Figure 1
Figure 1. Figure 1: FIG. 1. Connected tree-level diagrams contributing to the equations of motion at order [PITH_FULL_IMAGE:figures/full_fig_p005_1.png] view at source ↗
read the original abstract

We recast Einstein's equations as ordinary integro-differential equations for the worldlines, integrating out the gravitational field by means of the Schwinger-Keldysh path integral. The same framework allows the gravitational waveform to be computed for unspecified orbits. The two computations are independent: solutions of the equations of motion can then be inserted to reconstruct the waveform for generic orbits. The derivation of the equations of motion does not require a map between scattering and bound-orbit observables. Thus, it could be implemented within an Effective One-Body-inspired framework, with the advantage that retardation and radiation effects are automatically included: no separation between potential and radiation modes is required. Conversely, the waveform computation may provide an alternative to the Effective One-Body approach, if supplemented by suitable resummation schemes. We emphasise that computations in this framework bypass the need for integration-by-parts identities, which are the main technical bottleneck in the computation of observables. In this paper, we outline the general framework and present a computational strategy at leading and next-to-leading order in the weak-field expansion.

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 / 0 minor

Summary. The manuscript outlines a framework that uses the Schwinger-Keldysh path integral to integrate out the gravitational field, recasting Einstein's equations as integro-differential equations for worldlines. It also describes an independent computation of gravitational waveforms for unspecified (generic) orbits. Solutions of the equations of motion can be inserted into the waveform formula. The derivation of the EOM is claimed not to require a scattering-to-bound map and the overall approach is said to bypass integration-by-parts identities. The paper presents the general framework and a computational strategy at leading and next-to-leading order in the weak-field expansion, with potential applications to Effective One-Body models.

Significance. If the outlined framework can be carried through with explicit derivations and verified computations, it would offer a conceptually distinct route to relativistic observables that automatically incorporates retardation and radiation reaction without mode separation. The asserted independence between the EOM and waveform calculations, together with the avoidance of IBP identities, would constitute a technical advantage for high-order calculations. The manuscript's emphasis on applicability within EOB-inspired schemes is a potentially useful connection to existing phenomenology.

major comments (2)
  1. [Abstract] Abstract: the central claim that 'computations in this framework bypass the need for integration-by-parts identities' is presented without any explicit derivation, equation, or worked example at LO or NLO. No concrete reduction step or consistency check is supplied that would allow verification that the path-integral procedure indeed eliminates the IBP bottleneck.
  2. [Abstract] Abstract, paragraph on the two independent computations: the statement that 'solutions of the equations of motion can then be inserted to reconstruct the waveform' is asserted without demonstration that the waveform formula is free of additional consistency conditions or that the integro-differential EOM solutions remain well-defined when inserted. No explicit waveform expression or insertion procedure is given.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for their detailed reading and for highlighting points where the abstract claims would benefit from additional clarification. The manuscript is framed as an outline of the general framework together with a computational strategy at LO and NLO; we address the two major comments below and indicate the revisions we will make.

read point-by-point responses

  1. Referee: [Abstract] Abstract: the central claim that 'computations in this framework bypass the need for integration-by-parts identities' is presented without any explicit derivation, equation, or worked example at LO or NLO. No concrete reduction step or consistency check is supplied that would allow verification that the path-integral procedure indeed eliminates the IBP bottleneck.

    Authors: The Schwinger-Keldysh construction integrates the gravitational field out of the path integral before any perturbative expansion in the weak-field parameter, directly producing an effective action whose stationary-phase condition yields integro-differential worldline equations. Because the reduction is performed at the level of the functional integral rather than through diagram-by-diagram manipulation of Feynman integrals, the usual IBP identities that arise in the latter approach are not encountered. We acknowledge, however, that the manuscript supplies no explicit LO or NLO calculation that would illustrate the absence of IBP steps. We will revise the abstract to state that this bypass is a structural feature of the framework whose concrete verification is reserved for subsequent explicit computations. revision: yes

  2. Referee: [Abstract] Abstract, paragraph on the two independent computations: the statement that 'solutions of the equations of motion can then be inserted to reconstruct the waveform' is asserted without demonstration that the waveform formula is free of additional consistency conditions or that the integro-differential EOM solutions remain well-defined when inserted. No explicit waveform expression or insertion procedure is given.

    Authors: Both the worldline effective action and the waveform observable are obtained from the same Schwinger-Keldysh generating functional; the waveform is therefore expressed directly in terms of the worldline trajectories that extremize that action. Insertion is therefore formally consistent by construction. We agree that the manuscript does not display an explicit waveform formula or insertion algorithm. We will add a short clarifying sentence in the abstract (and, if space permits, in the introduction) noting that well-definedness follows from the common origin of the two quantities and that explicit insertion checks will be presented in follow-up work. revision: yes

Circularity Check

0 steps flagged

No significant circularity identified

full rationale

The abstract and outline describe a framework that recasts Einstein's equations via the Schwinger-Keldysh path integral into integro-differential worldline equations and computes waveforms independently, with explicit statements that the two computations are separate, no scattering-to-bound map is required, and IBP identities are bypassed. No equations, fitted parameters, self-citations, or ansatze are presented that reduce any claimed result to its inputs by construction. The derivation chain is therefore self-contained against the external path-integral formalism and does not exhibit any of the enumerated circularity patterns.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 0 invented entities

Review performed on abstract only; full paper may introduce additional parameters or assumptions not visible here.

axioms (1)
  • domain assumption Schwinger-Keldysh path integral yields classical integro-differential equations for worldlines after integrating out the gravitational field
    Central premise stated in the abstract for deriving the equations of motion.

pith-pipeline@v0.9.1-grok · 5701 in / 1302 out tokens · 23910 ms · 2026-06-27T12:04:10.877798+00:00 · methodology

discussion (0)

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Reference graph

Works this paper leans on

145 extracted references · 1 canonical work pages

  1. [1]

    In the classical limit, the SK formalism provides a systematic way to compute observables by iterating the equations of motion, restricting the diagram- matic expansion to vertices that involve only one advanced field

  2. [2]

    quantising

    The EoM for the causal fieldϕ+ are obtained by computing the one-point function of the fieldϕ−. In the two-body problem, the dynamical variables of interest are the perturbation of the metric around Minkowski space, gµν =η µν+κh µν ,(II.4) and the worldline variables of the two bodies, denoted byx µ i (λ), whereλis a parameter on the worldline. The action...

  3. [3]

    K. S. Thorne, Rev. Mod. Phys.52, 299 (1980)

    1980

  4. [4]

    Blanchet and T

    L. Blanchet and T. Damour, Phil. Trans. Roy. Soc. Lond. A320, 379 (1986)

    1986

  5. [5]

    Blanchet and T

    L. Blanchet and T. Damour, Phys. Rev. D37, 1410 (1988)

    1988

  6. [6]

    Blanchet and T

    L. Blanchet and T. Damour, Ann. Inst. H. Poincare Phys. Theor.50, 377 (1989)

    1989

  7. [7]

    Blanchet and T

    L. Blanchet and T. Damour, Phys. Rev. D46, 4304 (1992)

    1992

  8. [8]

    Blanchet, Living Rev

    L. Blanchet, Living Rev. Rel.17, 2 (2014), arXiv:1310.1528 [gr-qc]

    Pith/arXiv arXiv 2014

  9. [9]

    D. Bini, T. Damour, and A. Geralico, Phys. Rev. D 108, 124052 (2023), arXiv:2309.14925 [gr-qc]

    arXiv 2023

  10. [10]

    D. Bini, T. Damour, S. De Angelis, A. Geralico, A. Herderschee, R. Roiban, and F. Teng, Phys. Rev. D109, 125008 (2024), arXiv:2402.06604 [hep-th]

    arXiv 2024

  11. [11]

    Georgoudis, C

    A. Georgoudis, C. Heissenberg, and R. Russo, Phys. Rev. D109, 106020 (2024), arXiv:2402.06361 [hep-th]

    arXiv 2024

  12. [12]

    D. Bini, T. Damour, and A. Geralico, (2026), arXiv:2604.21522 [gr-qc]

    Pith/arXiv arXiv 2026

  13. [13]

    Blanchet, G

    L. Blanchet, G. Faye, Q. Henry, F. Larrouturou, and D. Trestini, Phys. Rev. Lett.131, 121402 (2023), arXiv:2304.11185 [gr-qc]

    arXiv 2023

  14. [14]

    Blanchet, G

    L. Blanchet, G. Faye, Q. Henry, F. Larrouturou, and D. Trestini, Phys. Rev. D108, 064041 (2023), arXiv:2304.11186 [gr-qc]

    arXiv 2023

  15. [15]

    W.D.GoldbergerandA.Ross,Phys.Rev.D81,124015 (2010), arXiv:0912.4254 [gr-qc]

    Pith/arXiv arXiv 2010

  16. [16]

    Ross, Phys

    A. Ross, Phys. Rev. D85, 125033 (2012), arXiv:1202.4750 [gr-qc]

    Pith/arXiv arXiv 2012

  17. [17]

    W. D. Goldberger and I. Z. Rothstein, Phys. Rev. D73, 104029 (2006), arXiv:hep-th/0409156

    Pith/arXiv arXiv 2006

  18. [18]

    R. A. Porto, M. M. Riva, and Z. Yang, JHEP04, 050 (2025), arXiv:2409.05860 [gr-qc]

    arXiv 2025

  19. [19]

    M.M.Ivanov, Y.-Z.Li, J.Parra-Martinez, andZ.Zhou, Phys. Rev. Lett.135, 141401 (2025), arXiv:2504.07862 [hep-th]

    Pith/arXiv arXiv 2025

  20. [20]

    Foffa, P

    S. Foffa, P. Mastrolia, R. Sturani, and C. Sturm, Phys. Rev. D95, 104009 (2017), arXiv:1612.00482 [gr-qc]

    Pith/arXiv arXiv 2017

  21. [21]

    Foffa and R

    S. Foffa and R. Sturani, Phys. Rev. D100, 024047 (2019), arXiv:1903.05113 [gr-qc]

    arXiv 2019

  22. [22]

    Foffa, R

    S. Foffa, R. A. Porto, I. Rothstein, and R. Sturani, Phys. Rev. D100, 024048 (2019), arXiv:1903.05118 [gr- qc]

    arXiv 2019

  23. [23]

    Foffa, P

    S. Foffa, P. Mastrolia, R. Sturani, C. Sturm, and W. J. Torres Bobadilla, Phys. Rev. Lett.122, 241605 (2019), arXiv:1902.10571 [gr-qc]

    Pith/arXiv arXiv 2019

  24. [24]

    Blümlein, A

    J. Blümlein, A. Maier, P. Marquard, and G. Schäfer, Nucl. Phys. B983, 115900 (2022), [Erratum: Nucl.Phys.B 985, 115991 (2022)], arXiv:2110.13822 [gr- qc]

    arXiv 2022

  25. [25]

    Brunello, M

    G. Brunello, M. K. Mandal, P. Mastrolia, R. Patil, M. Pegorin, J. Ronca, S. Smith, J. Steinhoff, and W. J. Torres Bobadilla, (2025), arXiv:2512.19498 [hep-th]

    arXiv 2025

  26. [26]

    R. A. Porto and M. M. Riva, (2026), arXiv:2604.09545 [gr-qc]

    Pith/arXiv arXiv 2026

  27. [27]

    Brunello, M

    G. Brunello, M. K. Mandal, P. Mastrolia, R. Patil, M. Pegorin, S. Smith, and J. Steinhoff, (2026), arXiv:2604.14134 [hep-th]

    Pith/arXiv arXiv 2026

  28. [28]

    Cheung, I

    C. Cheung, I. Z. Rothstein, and M. P. Solon, Phys. Rev. Lett.121, 251101 (2018), arXiv:1808.02489 [hep-th]

    Pith/arXiv arXiv 2018

  29. [29]

    Zeng, Phys

    Z.Bern, C.Cheung, R.Roiban, C.-H.Shen, M.P.Solon, and M. Zeng, Phys. Rev. Lett.122, 201603 (2019), arXiv:1901.04424 [hep-th]

    Pith/arXiv arXiv 2019

  30. [30]

    J. S. Schwinger, J. Math. Phys.2, 407 (1961)

    1961

  31. [31]

    P. M. Bakshi and K. T. Mahanthappa, J. Math. Phys. 4, 1 (1963)

    1963

  32. [32]

    P. M. Bakshi and K. T. Mahanthappa, J. Math. Phys. 4, 12 (1963)

    1963

  33. [33]

    L. V. Keldysh, Zh. Eksp. Teor. Fiz.47, 1515 (1964)

    1964

  34. [34]

    C. R. Galley and M. Tiglio, Phys. Rev. D79, 124027 (2009), arXiv:0903.1122 [gr-qc]

    Pith/arXiv arXiv 2009

  35. [35]

    C. R. Galley, Phys. Rev. Lett.110, 174301 (2013), arXiv:1210.2745 [gr-qc]

    Pith/arXiv arXiv 2013

  36. [36]

    G. U. Jakobsen, G. Mogull, J. Plefka, and B. Sauer, JHEP10, 128 (2022), arXiv:2207.00569 [hep-th]

    arXiv 2022

  37. [37]

    Kälin, J

    G. Kälin, J. Neef, and R. A. Porto, JHEP01, 140 (2023), arXiv:2207.00580 [hep-th]

    arXiv 2023

  38. [38]

    Kälin and R

    G. Kälin and R. A. Porto, JHEP11, 106 (2020), arXiv:2006.01184 [hep-th]

    arXiv 2020

  39. [39]

    D. Bini, T. Damour, and A. Geralico, Phys. Rev. D 110, 104051 (2024), arXiv:2408.17193 [gr-qc]

    arXiv 2024

  40. [40]

    Mogull, J

    G. Mogull, J. Plefka, and K. Stoldt, Phys. Rev. D112, 124076 (2025), arXiv:2506.20643 [hep-th]

    arXiv 2025

  41. [41]

    Brandhuber, G

    A. Brandhuber, G. R. Brown, G. Chen, S. De Angelis, J. Gowdy, and G. Travaglini, JHEP06, 048 (2023), arXiv:2303.06111 [hep-th]

    arXiv 2023

  42. [42]

    Herderschee, R

    A. Herderschee, R. Roiban, and F. Teng, JHEP06, 004 (2023), arXiv:2303.06112 [hep-th]

    arXiv 2023

  43. [43]

    Georgoudis, C

    A. Georgoudis, C. Heissenberg, and I. Vazquez-Holm, JHEP06, 126 (2023), arXiv:2303.07006 [hep-th]

    arXiv 2023

  44. [44]

    Elkhidir, D

    A. Elkhidir, D. O’Connell, M. Sergola, and I. A. Vazquez-Holm, JHEP07, 272 (2024), arXiv:2303.06211 [hep-th]

    arXiv 2024

  45. [45]

    Bohnenblust, H

    L. Bohnenblust, H. Ita, M. Kraus, and J. Schlenk, JHEP12, 100 (2025), arXiv:2505.15724 [hep-th]

    arXiv 2025

  46. [46]

    Brunello, S

    G. Brunello, S. De Angelis, and D. A. Kosower, (2025), arXiv:2511.05412 [hep-th]

    arXiv 2025

  47. [47]

    Damour, Phys

    T. Damour, Phys. Rev. D94, 104015 (2016), arXiv:1609.00354 [gr-qc]

    Pith/arXiv arXiv 2016

  48. [48]

    Damour, Phys

    T. Damour, Phys. Rev. D97, 044038 (2018), arXiv:1710.10599 [gr-qc]

    Pith/arXiv arXiv 2018

  49. [49]

    Z. Bern, L. J. Dixon, D. C. Dunbar, and D. A. Kosower, Nucl. Phys. B425, 217 (1994), arXiv:hep-ph/9403226

    Pith/arXiv arXiv 1994

  50. [50]

    Z. Bern, L. J. Dixon, D. C. Dunbar, and D. A. Kosower, Nucl. Phys. B435, 59 (1995), arXiv:hep-ph/9409265

    Pith/arXiv arXiv 1995

  51. [51]

    Z. Bern, L. J. Dixon, and D. A. Kosower, Nucl. Phys. B513, 3 (1998), arXiv:hep-ph/9708239. 10

    Pith/arXiv arXiv 1998

  52. [52]

    Mogull, J

    G. Mogull, J. Plefka, and J. Steinhoff, JHEP02, 048 (2021), arXiv:2010.02865 [hep-th]

    arXiv 2021

  53. [53]

    Parra-Martinez, M

    J. Parra-Martinez, M. S. Ruf, and M. Zeng, JHEP11, 023 (2020), arXiv:2005.04236 [hep-th]

    arXiv 2020

  54. [54]

    Cheung and M

    C. Cheung and M. P. Solon, JHEP06, 144 (2020), arXiv:2003.08351 [hep-th]

    arXiv 2020

  55. [55]

    Di Vecchia, C

    P. Di Vecchia, C. Heissenberg, R. Russo, and G. Veneziano, JHEP07, 169 (2021), arXiv:2104.03256 [hep-th]

    arXiv 2021

  56. [56]

    N. E. J. Bjerrum-Bohr, P. H. Damgaard, L. Planté, and P. Vanhove, JHEP08, 172 (2021), arXiv:2105.05218 [hep-th]

    arXiv 2021

  57. [57]

    Brandhuber, G

    A. Brandhuber, G. Chen, G. Travaglini, and C. Wen, JHEP10, 118 (2021), arXiv:2108.04216 [hep-th]

    arXiv 2021

  58. [58]

    Kälin, Z

    G. Kälin, Z. Liu, and R. A. Porto, Phys. Rev. Lett. 125, 261103 (2020), arXiv:2007.04977 [hep-th]

    arXiv 2020

  59. [59]

    Dlapa, G

    C. Dlapa, G. Kälin, Z. Liu, and R. A. Porto, Phys. Lett. B831, 137203 (2022), arXiv:2106.08276 [hep-th]

    arXiv 2022

  60. [60]

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

    arXiv 2021

  61. [61]

    Dlapa, G

    C. Dlapa, G. Kälin, Z. Liu, J. Neef, and R. A. Porto, Phys. Rev. Lett.130, 101401 (2023), arXiv:2210.05541 [hep-th]

    arXiv 2023

  62. [62]

    G. U. Jakobsen, G. Mogull, J. Plefka, B. Sauer, and Y. Xu, Phys. Rev. Lett.131, 151401 (2023), arXiv:2306.01714 [hep-th]

    arXiv 2023

  63. [63]

    G. U. Jakobsen, G. Mogull, J. Plefka, and B. Sauer, Phys. Rev. Lett.131, 241402 (2023), arXiv:2308.11514 [hep-th]

    arXiv 2023

  64. [64]

    P. H. Damgaard, E. R. Hansen, L. Planté, and P. Van- hove, JHEP09, 183 (2023), arXiv:2307.04746 [hep-th]

    arXiv 2023

  65. [65]

    Driesse, G

    M. Driesse, G. U. Jakobsen, G. Mogull, J. Plefka, B. Sauer, and J. Usovitsch, Phys. Rev. Lett.132, 241402 (2024), arXiv:2403.07781 [hep-th]

    arXiv 2024

  66. [66]

    Driesse, G

    M. Driesse, G. U. Jakobsen, A. Klemm, G. Mogull, C. Nega, J. Plefka, B. Sauer, and J. Usovitsch, Nature 641, 603 (2025), arXiv:2411.11846 [hep-th]

    Pith/arXiv arXiv 2025

  67. [67]

    Z. Bern, E. Herrmann, R. Roiban, M. S. Ruf, A. V. Smirnov, V. A. Smirnov, and M. Zeng, Phys. Rev. Lett. 136, 081401 (2026), arXiv:2509.17412 [hep-th]

    arXiv 2026

  68. [68]

    Z. Bern, E. Herrmann, R. Roiban, M. S. Ruf, A. V. Smirnov, S. Smith, and M. Zeng, (2025), arXiv:2512.23654 [hep-th]

    arXiv 2025

  69. [69]

    Driesse, G

    M. Driesse, G. U. Jakobsen, G. Mogull, C. Nega, J. Plefka, B. Sauer, and J. Usovitsch, (2026), arXiv:2601.16256 [hep-th]

    arXiv 2026

  70. [70]

    Barack and A

    L. Barack and A. Pound, Rept. Prog. Phys.82, 016904 (2019), arXiv:1805.10385 [gr-qc]

    Pith/arXiv arXiv 2019

  71. [71]

    Pound and B

    A. Pound and B. Wardell, (2021), 10.1007/978-981-15- 4702-7_38-1, arXiv:2101.04592 [gr-qc]

    work page doi:10.1007/978-981-15- 2021

  72. [72]

    Warburton, A

    N. Warburton, A. Pound, B. Wardell, J. Miller, and L. Durkan, Phys. Rev. Lett.127, 151102 (2021), arXiv:2107.01298 [gr-qc]

    arXiv 2021

  73. [73]

    Wardell, A

    B. Wardell, A. Pound, N. Warburton, J. Miller, L. Durkan, and A. Le Tiec, Phys. Rev. Lett.130, 241402 (2023), arXiv:2112.12265 [gr-qc]

    arXiv 2023

  74. [74]

    Mathews, B

    J. Mathews, B. Wardell, A. Pound, and N. Warburton, Phys. Rev. D113, 064034 (2026), arXiv:2510.16113 [gr- qc]

    Pith/arXiv arXiv 2026

  75. [75]

    Honet, J

    L. Honet, J. Mathews, G. Compère, A. Pound, B. Wardell, G. A. Piovano, M. van de Meent, and N. Warburton, (2025), arXiv:2510.16112 [gr-qc]

    arXiv 2025

  76. [76]

    Mathews and A

    J. Mathews and A. Pound, Phys. Rev. D112, 104078 (2025), arXiv:2501.01413 [gr-qc]

    arXiv 2025

  77. [77]

    Warburton, Phys

    N. Warburton, Phys. Rev. D113, 084059 (2026), arXiv:2512.02274 [gr-qc]

    Pith/arXiv arXiv 2026

  78. [78]

    Barack, R

    L. Barack, R. Gonzo, B. Leather, O. Long, and N. Warburton, Phys. Rev. D113, 104042 (2026), arXiv:2602.10089 [gr-qc]

    Pith/arXiv arXiv 2026

  79. [79]

    Geralico, (2026), arXiv:2603.11774 [gr-qc]

    A. Geralico, (2026), arXiv:2603.11774 [gr-qc]

    arXiv 2026

  80. [80]

    Buonanno and T

    A. Buonanno and T. Damour, Phys. Rev. D59, 084006 (1999), arXiv:gr-qc/9811091

    Pith/arXiv arXiv 1999

Showing first 80 references.