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A universal logarithmic divergence near the scattering-plunge boundary anchors new analytic interpolation formulas for gravitational-wave energy loss, matching numerical results to within roughly 10-25% across all parameter space.

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2026-08-03 01:15 UTC pith:JHFCQKTK

load-bearing objection Genuinely new and mostly sound resummation for E+ energy loss; the E- horizon channel rests on an ad hoc one-velocity fit and the uniform-validity claim overreaches. the 3 major comments →

arxiv 2602.10089 v2 pith:JHFCQKTK submitted 2026-02-10 gr-qc hep-th

Resummed energy loss in extreme-mass-ratio scattering using critical orbits

Leor Barack , Riccardo Gonzo , Benjamin Leather , Oliver Long , Niels Warburton This is my paper
classification gr-qc hep-th MSC 83C1083C2583C3583C57 PACS 04.25.-g04.30.-w04.70.-s
keywords extreme-mass-ratio scatteringgravitational-wave energy lossseparatrixzoom-whirl orbitspost-Minkowskian expansionpost-Newtonian expansionblack hole perturbation theoryresummation
verification ladder T0 review T1 audit T2 compute T3 formal T4 reserved

The pith

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

This paper aims to bridge weak-field and strong-field descriptions of black-hole binary dynamics. It claims that the energy radiated by a small body scattering off a Schwarzschild black hole diverges logarithmically as the orbit approaches the separatrix, and that the coefficient of that divergence can be obtained from unstable-circular-orbit fluxes. Using this as a strong-field anchor, the authors resum post-Minkowskian and post-Newtonian expansions into semi-analytic formulas for the energy emitted to infinity and absorbed by the horizon. Tested against high-precision numerical perturbation results, the formulas stay uniformly reliable across the scattering parameter space, with the mixed resummation matching exact values to within roughly 10% at low velocity and 25% at v=0.7. If correct, this offers a systematic route to uniformly valid models of radiative observables, including bound orbits.

Core claim

This paper establishes that the total gravitational-wave energy emitted by a small body scattering off a Schwarzschild black hole has a universal logarithmic divergence as the orbit approaches the separatrix between scattering and plunge, with the coefficient fixed by the energy flux of the limiting unstable circular geodesic. The authors compute those circular-orbit fluxes to high precision for radii 3M < R ≤ 6M, fit them to analytic rational-log models, and add the resulting singular term to state-of-the-art post-Minkowskian and post-Newtonian expansions for the energy radiated to infinity and absorbed by the horizon, subtracting counterterms so that all known weak-field coefficients are p

What carries the argument

The central object is the separatrix—the curve in (v,j) parameter space separating scattering from plunging geodesics—and the logarithmic divergence of radiated energy near it: E±_GW ≃ − R^{3/2}(6M−R)^{-1/2} F±_o(R) log(δj/j_c(v)) + const±. The coefficient B±(v) is fixed by F±_o(R), the gravitational-wave energy flux of the unstable circular geodesic at the whirl radius R, computed numerically and fitted to an analytic rational-log model. The resummation uses \tilde E±_X = E±_X + E±_sing − CT±_X: the singular term is added to a base PM or mixed PM/PN expansion, and counterterms are subtracted so existing weak-field terms remain untouched. For the horizon term, an exponential attenuation repl

Load-bearing premise

The construction assumes the radiated energy near the separatrix is dominated by the near-circular whirl motion, so the coefficient of the logarithmic divergence is fixed entirely by the instantaneous flux of the limiting unstable circular geodesic, with the rest of the orbit contributing only bounded, non-logarithmic terms; it also assumes a fixed geodesic with no radiation reaction.

What would settle it

For a fixed scattering geodesic at, say, v=0.2 and δj/j_c as small as 10^-4, compute the full numerical E+_GW and check whether E+_GW − B+(v) log(δj/j_c) tends to a finite constant as δj→0. If a residual logarithmic growth appears, or if the slope does not match the circular-orbit-flux value B+(v), the anchor fails; a second logarithmic contribution or a divergent radiation-reaction correction at this order would also falsify it.

Watch this falsifier — get emailed when new claim-graph text bears on it.

If this is right

  • The mixed 5PM/3′PN resummation \tilde E^+_mixed reproduces the numerical energy flux to infinity within ~10% at v=0.2, within ~15% at v=0.35, and within ~25% at v=0.7 across the full domain down to the separatrix.
  • The horizon-absorbed energy can be resummed with an exponential attenuation, and using numerically fitted 8PM and 9PM coefficients improves the match at v=0.35.
  • The procedure preserves all known PM and PN coefficients, since it only adds the singular term and subtracts its own expansion.
  • The same separatrix-anchored approach is expected to apply to other scattering observables such as angular-momentum loss, time delay, and redshift, and, via scattering-to-bound mapping or direct resummation, to bound-orbit radiative observables.

Where Pith is reading between the lines

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

  • Inference: If a similar logarithmic anchor exists for unstable circular orbits of Kerr black holes, the method could produce uniformly valid energy-loss models for spinning extreme-mass-ratio inspirals without requiring new full-waveform information.
  • Inference: A next-order singular term beyond the leading log could be extracted numerically and added to the resummation, potentially cutting the residual below the current 10-25% band.
  • Inference: The cleanest stress test would be the ultrarelativistic regime v ≳ 0.97, where the flux fit is least refined and higher PM orders matter; accuracy there may degrade below the paper's stated levels.
  • Inference: The success of the mixed resummation suggests that a purely local strong-field condition—the singular flux—can fix a global interpolation, a principle that may guide models of other two-body radiative observables.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit.

Referee Report

3 major / 4 minor

Summary. The paper constructs resummed, semi-analytic approximations for the leading self-force-order gravitational energy lost to infinity (E+) and into the horizon (E-) in extreme-mass-ratio scattering off a Schwarzschild black hole. The method uses the logarithmic divergence of the energy loss near the scattering/plunge separatrix, whose coefficient is fixed by circular-orbit fluxes on the unstable circular orbit, and blends this singular term with known PM and PN weak-field expansions via counterterm subtraction. The E+ resummation is benchmarked against independent black-hole perturbation theory data at v=0.2, 0.35, and 0.7, with stated agreement of about 10%, 15%, and 25%, respectively. The E- resummation abandons the counterterm procedure and instead uses a phenomenological exponential attenuation, tuned and tested at a single velocity v=0.35. The paper claims the resulting formulas are uniformly reliable across the full scattering parameter space, and suggests extensions to bound orbits and other observables.

Significance. If the claims hold, this is a useful and conceptually attractive bridge between weak-field PM/PN expansions and strong-field separatrix behavior for radiative observables. The core derivation of the logarithmic singular anchor is clean, and the use of independent, high-precision circular-orbit flux data as input is a genuine strength; the flux fit is validated to better than 10^-6 over most of its stated range. The E+ mixed resummation is tested at three velocities and appears to interpolate the numerical data across the whole weak-to-strong-field domain. The paper also provides ancillary data and scripts, which supports reproducibility. However, the E- channel is only demonstrated at one velocity and uses an explicitly ad hoc attenuation, so the 'full parameter space' claim, which covers both channels, is not yet supported. The fixed-geodesic assumption underlying the singular anchor is acknowledged but not fully justified for matching to the physical retarded PM energy loss.

major comments (3)
  1. [§VI, Eq. (49), Fig. 8] The horizon-absorption resummation E- is load-bearing for the paper's central claim, yet it is validated at a single velocity (v=0.35). The exponential attenuation in Eq. (49) has beta=1/2 selected 'through experiment' and k fixed by Eq. (50) from the difference |E_PM - E_sing|; the reported k=13.8894 is for that one curve. There is no test at v=0.2 or v=0.7 analogous to Figs. 5-7 for E+. The abstract and Sec. VII assert uniform reliability across the full scattering parameter space for the energy down the horizon, but this is not demonstrated. I request additional benchmarks at multiple velocities (including small and large v) or, failing that, a revised claim that the E- approximation is demonstrated only near v=0.35.
  2. [§III.A, Eqs. (26)-(28)] The divergent coefficient B±(v) is derived for a fixed geodesic with no radiation reaction, which the authors note is only consistent with time-symmetric boundary conditions. The quantity being resummed, however, is the physical energy loss computed with retarded boundary conditions in the PM/SF framework. It is not automatic that the coefficient of the log divergence in the physical quantity is identical to that of the fixed-geodesic source, since radiation reaction can shift the effective separatrix or introduce additional logarithmic corrections. The authors should either prove that the fixed-geodesic leading log survives in the self-force-corrected observable, or provide a numerical check of Eq. (28) against a small-δj self-force calculation at a couple of velocities. This is central because Eq. (28) is the anchor for both E+ and E- resummations.
  3. [§III.B, Eq. (31), Fig. 2] The flux fit (31) is validated only for 3.02M ≲ R ≤ 6M, i.e. v ≲ 0.97, as the text states. The ultra-relativistic tail R→3M (v→1) is left open, and the fit is acknowledged to be refinable near R=3M. Since the paper claims uniform reliability across the full scattering parameter space, the absence of any test above v≈0.97 is a gap, especially because the singular coefficient B±(v) is extrapolated there. Either extend the high-precision flux computation closer to the light ring and test the resummation at v=0.9 or higher, or explicitly restrict the claimed domain of validity.
minor comments (4)
  1. [§II.A, Eq. (19)] The displayed expansion for the radial action appears garbled: 'c^{(\bar r)}_{log}(v)δj log(δj/j_c(v))' reads as if the coefficient multiplies δj inside and outside the log; this should be cleaned up.
  2. [§II, Eq. (13)] The definition p_c(e)=6+2e is introduced without derivation; a brief parenthetical explanation or reference would help the reader.
  3. [§VI, Fig. 8] The figure includes 8PM and 9PM 'predictions' extracted from numerical data, but the text does not specify how the fit was performed or what the resulting coefficients are. Since this is a side demonstration, a sentence describing the fit procedure or pointing to the accompanying script would suffice.
  4. [Conventions and notation] The symbol E is used for both the specific energy and the radiated energy E_GW; the notation is standard but occasionally confusing (e.g., E+_GW and E+_PM are introduced without a table). A short notation glossary would improve readability.

Circularity Check

2 steps flagged

Core resummation is not circular: the separatrix coefficient is anchored in independently computed circular-orbit fluxes and the asymptotic matching is openly built by construction; only minor self-citation and one by-design boundary condition prevent a clean zero.

specific steps
  1. self definitional [Sec. VI, Fig. 5 discussion (after Eq. 44)]
    "By design, the resummation formulas both agree with the exact values E + GW in the asymptotic domains δj→0 and δj→∞, but we see in this example how they succeed in tracking the correct behavior uniformly well at any δj."

    This asymptotic agreement is definitional: Eq. (44), E~±_X = E±_X + E±_sing − CT±_X, adds the singular log term and subtracts its PM/PN expansion, so the model must reduce to E±_X at δj→∞ and to B±(v) log(δj/jc) at δj→0. The matching at the two ends is therefore not an independent numerical prediction; the genuinely predictive content is the intermediate-δj behavior. The paper explicitly labels this 'By design', so it is a structural caveat rather than a hidden derivation loop.

  2. self citation load bearing [Sec. II, Eq. (16), with use in Eqs. (26)-(28)]
    "The coefficient of the logarithmic term in Eq. (15) is A(v) = −(1− 12/j2c(v))^{−1/4}, a derivation of which can be found in Appendix A of [39]."

    A(v) enters Eq. (26) and thereby fixes the strength of the entire separatrix anchor E±_sing in Eq. (28). Ref. [39] (Long, Whittall, Barack) includes two of the present authors, so a load-bearing strong-field input is invoked from the authors' own prior work rather than rederived here. This is a genuine self-citation, but the result is parameter-free and independently rederivable from the radial action; it is not fitted to the target scattering energy, so the circularity is nominal and does not undermine the independent benchmark tests.

full rationale

The paper's central derivation is self-contained against external benchmarks. The logarithmic coefficient B±(v) in Eq. (43) is built from circular-orbit fluxes F±_◦(R), which are computed with an independent hyperboloidal-spectral code [65] and fit to their own numerical data (Eq. 31, Table I); these data are not the scattering energy-loss values E±_GW. The weak-field inputs (5PM, 3'PN, 7PM) come from external PM/PN calculations, and the numerical scattering benchmarks come from the independent code of Ref. [55]. Thus the resummation is not fitting E±_GW and then re-deriving it. The only by-construction element is the asymptotic matching, which the paper openly admits; the non-trivial claim is the 10–25% intermediate agreement, which is genuine. For the horizon channel, Eq. (49) with β=1/2 chosen 'through experiment' and demonstrated only at v=0.35 is a support/robustness gap for the 'full parameter space' claim, but it is not circular: k and β are set from E−_PM and E−_sing, not fitted to E−_GW. Overall score 2: one minor self-citation and one definitional boundary condition, with the central predictive content independent.

Axiom & Free-Parameter Ledger

5 free parameters · 7 axioms · 0 invented entities

The central claim leans on the analytic structure of Schwarzschild geodesics (standard), on the a priori known log divergence of near-separatrix radiation (derived here from the radial action, matching Ref. [54]), and on numerically fitted input: 32 coefficients of the circular-flux model (Table I) that fix the singular anchor, plus the hand-chosen attenuation for horizon absorption. No new physical entities are introduced.

free parameters (5)
  • Circular-flux fit coefficients a+/-_i, b+/-_i (i=0..5), c+/-_i (i=0..3) = Table I (16 per flux, 32 total)
    Non-linear least-squares fit of Eq. (31) to numerically computed F+/-_o(R); these set B+/-(v) in (43), the strength of the singular anchor of the whole resummation.
  • Exponential attenuation exponent beta for horizon absorption = beta = 1/2
    Chosen by experiment in Sec. VI: 'beta=1 acts too aggressively... beta=1/2 was selected'.
  • Exponential attenuation scale k for horizon absorption = k = 3*sqrt(jc/delta_j0); 13.8894 at v=0.35
    Prescribed by a 3-exponential-folds rule at j0; the fold count is hand-set and the demonstration is at one velocity.
  • Fit-model polynomial orders and validation window = P5/P3; 3.02M <= R <= 6M
    Orders selected to minimise residuals; the fit is not validated for v > 0.97 (R < 3.02M).
  • 8PM and 9PM E-_GW coefficients (Fig. 8 demonstration) = not given in text; from Ref. [55]
    Obtained by fitting a higher-order PM model to large-j numerical E-_GW data; used only in the auxiliary demonstration, and labelled 'predict' by the authors themselves.
axioms (7)
  • domain assumption Schwarzschild geodesic dynamics: first integrals (2), effective potential (3), separatrix j_c(v) (10)-(11)
    General relativity on Schwarzschild; the test-particle limit q->0. Standard background used throughout Secs. II-III.
  • domain assumption Balance-law formula E_GW = -m integral Edot dtau (Eq. 21)
    Quinn-Wald energy balance [63] applied per geodesic; standard in the self-force literature.
  • ad hoc to paper Fixed geodesic with no radiation reaction even as delta j -> 0 (Sec. III.A)
    Authors acknowledge this 'must ultimately fail' physically and is consistent only with time-symmetric boundary conditions; it underlies the singular formula (28).
  • standard math Near-separatrix azimuthal divergence Delta phi ~ A(v) log(delta j/j_c) (Eqs. 15-17)
    Derived in Appendix A of Ref. [39] via the radial action; re-derived here from the branch-cut structure (Sec. II.A).
  • domain assumption Energy-balance identity -m Edot_o = (1-3M/R)^(-1/2)(F+_o + F-_o) (Eq. 27)
    Bound-orbit energy balance [64] applied to the limiting circular geodesic.
  • domain assumption Flux divergence near the light ring F+/-_o ~ (log z)/z as z -> 0 (Sec. III.B)
    Taken from Ref. [54]; used to fix the functional form of the fit model (31).
  • ad hoc to paper Rational-log model (31) with chosen polynomial orders
    Phenomenological fit form selected to match PN behavior (alpha+ = 5, alpha- = 9) and the light-ring log divergence; orders chosen to minimize residuals.

pith-pipeline@v1.3.0-alltime-deepseek · 21486 in / 21257 out tokens · 219539 ms · 2026-08-03T01:15:58.624088+00:00 · methodology

0 comments
read the original abstract

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.

Figures

Figures reproduced from arXiv: 2602.10089 by Benjamin Leather, Leor Barack, Niels Warburton, Oliver Long, Riccardo Gonzo.

Figure 1
Figure 1. Figure 1: FIG. 1. Representation of the space of (non-plunging) [PITH_FULL_IMAGE:figures/full_fig_p003_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: FIG. 2. Energy flux (per [PITH_FULL_IMAGE:figures/full_fig_p006_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: FIG. 3. Total energy radiated to infinity in the weak-field [PITH_FULL_IMAGE:figures/full_fig_p009_3.png] view at source ↗
Figure 5
Figure 5. Figure 5: displays the resummed energy-loss expres￾sions E˜+ PM and E˜+ mixed as functions of δj := j − jc(v) for a fixed velocity-at-infinity value of v = 0.2. Also shown, for reference, are the plain 5PM and 5PM/3′PN approximations (without resummation), and the compar￾ison numerical results for a sample of δj values. By de￾sign, the resummation formulas both agree with the ex￾act values E + GW in the asymptotic d… view at source ↗
Figure 8
Figure 8. Figure 8: FIG. 8. Resummed horizon absorption models [PITH_FULL_IMAGE:figures/full_fig_p011_8.png] view at source ↗
Figure 7
Figure 7. Figure 7: FIG. 7. Same as in Figs [PITH_FULL_IMAGE:figures/full_fig_p011_7.png] view at source ↗

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Forward citations

Cited by 2 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score.

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Reference graph

Works this paper leans on

89 extracted references · 66 linked inside Pith · cited by 2 Pith papers

  1. [1]

    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

  2. [2]

    Colpiet al.(LISA), LISA Definition Study Report, (2024), arXiv:2402.07571 [astro-ph.CO]

    M. Colpiet al.(LISA), LISA Definition Study Report, (2024), arXiv:2402.07571 [astro-ph.CO]

    Pith/arXiv arXiv 2024

  3. [3]

    A. G. Abacet al.(LIGO Scientific, VIRGO, KAGRA), GW231123: A Binary Black Hole Merger with Total Mass 190–265 M ⊙, Astrophys. J. Lett.993, L25 (2025), arXiv:2507.08219 [astro-ph.HE]

    Pith/arXiv arXiv 2025

  4. [4]

    Barack and A

    L. Barack and A. Pound, Self-force and radiation reac- tion in general relativity, Rept. Prog. Phys.82, 016904 (2019), arXiv:1805.10385 [gr-qc]

    Pith/arXiv arXiv 2019

  5. [5]

    Pound and B

    A. Pound and B. Wardell, Black hole perturbation the- ory and gravitational self-force, (2021), arXiv:2101.04592 [gr-qc]

    Pith/arXiv arXiv 2021

  6. [6]

    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

  7. [7]

    Buonanno, M

    A. Buonanno, M. Khalil, D. O’Connell, R. Roiban, M. P. Solon, and M. Zeng, Snowmass White Paper: Gravita- tional Waves and Scattering Amplitudes, inSnowmass 2021(2022) arXiv:2204.05194 [hep-th]

    Pith/arXiv arXiv 2021

  8. [8]

    Di Vecchia, C

    P. Di Vecchia, C. Heissenberg, R. Russo, and G. Veneziano, The gravitational eikonal: From parti- cle, string and brane collisions to black-hole encounters, Phys. Rept.1083, 1 (2024), arXiv:2306.16488 [hep-th]

    Pith/arXiv arXiv 2024

  9. [9]

    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

  10. [10]

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

    Pith/arXiv arXiv 2019

  11. [11]

    Damour, Radiative contribution to classical gravita- tional scattering at the third order inG, Phys

    T. Damour, Radiative contribution to classical gravita- tional scattering at the third order inG, Phys. Rev. D 102, 124008 (2020), arXiv:2010.01641 [gr-qc]

    Pith/arXiv arXiv 2020

  12. [12]

    Di Vecchia, C

    P. Di Vecchia, C. Heissenberg, R. Russo, and G. Veneziano, The eikonal approach to gravitational scattering and radiation atO(G 3), JHEP07, 169, arXiv:2104.03256 [hep-th]

    Pith/arXiv arXiv

  13. [13]

    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 atO(G 4), Phys. Rev. Lett.126, 171601 (2021), arXiv:2101.07254 [hep-th]

    Pith/arXiv arXiv 2021

  14. [14]

    Z. Bern, J. Parra-Martinez, R. Roiban, M. S. Ruf, C.- H. Shen, M. P. Solon, and M. Zeng, Scattering Am- plitudes, the Tail Effect, and Conservative Binary Dy- namics at O(G4), Phys. Rev. Lett.128, 161103 (2022), arXiv:2112.10750 [hep-th]

    Pith/arXiv arXiv 2022

  15. [15]

    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]

    Pith/arXiv arXiv 2022

  16. [16]

    Dlapa, G

    C. Dlapa, G. K¨ alin, Z. Liu, and R. A. Porto, Con- servative Dynamics of Binary Systems at Fourth Post- Minkowskian Order in the Large-Eccentricity Expansion, Phys. Rev. Lett.128, 161104 (2022), arXiv:2112.11296 [hep-th]

    Pith/arXiv arXiv 2022

  17. [17]

    Dlapa, G

    C. Dlapa, G. K¨ alin, Z. Liu, and R. A. Porto, Lo- cal in Time Conservative Binary Dynamics at Fourth Post-Minkowskian Order, Phys. Rev. Lett.132, 221401 (2024), arXiv:2403.04853 [hep-th]

    Pith/arXiv arXiv 2024

  18. [18]

    Driesse, G

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

    Pith/arXiv arXiv 2025

  19. [19]

    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]

    Pith/arXiv arXiv 2024

  20. [20]

    Dlapa, G

    C. Dlapa, G. K¨ alin, Z. Liu, and R. A. Porto, Local- in-Time Conservative Binary Dynamics at Fifth Post- Minkowskian and First Self-Force Orders, (2025), arXiv:2506.20665 [hep-th]

    Pith/arXiv arXiv 2025

  21. [21]

    Z. Bern, E. Herrmann, R. Roiban, M. S. Ruf, A. V. Smirnov, S. Smith, and M. Zeng, Scattering Amplitudes and Conservative Binary Dynamics atO(G 5) without Self-Force Truncation, (2025), arXiv:2512.23654 [hep- th]

    arXiv 2025

  22. [22]

    Driesse, G

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

    Pith/arXiv arXiv 2026

  23. [23]

    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

  24. [24]

    Damour, Classical and quantum scattering in post- Minkowskian gravity, Phys

    T. Damour, Classical and quantum scattering in post- Minkowskian gravity, Phys. Rev. D102, 024060 (2020), arXiv:1912.02139 [gr-qc]

    Pith/arXiv arXiv 2020

  25. [25]

    Antonelli, A

    A. Antonelli, A. Buonanno, J. Steinhoff, M. van de Meent, and J. Vines, Energetics of two-body Hamilto- nians in post-Minkowskian gravity, Phys. Rev. D99, 104004 (2019), arXiv:1901.07102 [gr-qc]

    Pith/arXiv arXiv 2019

  26. [26]

    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]

    Pith/arXiv arXiv 2022

  27. [27]

    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]

    Pith/arXiv arXiv 2024

  28. [28]

    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]

    Pith/arXiv arXiv 2024

  29. [29]

    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, (2025), arXiv:2507.08071 [gr- qc]

    arXiv 2025

  30. [30]

    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

  31. [31]

    K¨ alin and R

    G. K¨ alin and R. A. Porto, From Boundary Data to Bound States, JHEP01, 072, arXiv:1910.03008 [hep-th]. 14

    Pith/arXiv arXiv 1910

  32. [32]

    G. Cho, G. K¨ alin, and R. A. Porto, From boundary data to bound states. Part III. Radiative effects, JHEP04, 154, [Erratum: JHEP 07, 002 (2022)], arXiv:2112.03976 [hep-th]

    Pith/arXiv arXiv 2022

  33. [33]

    M. V. S. Saketh, J. Vines, J. Steinhoff, and A. Buonanno, Conservative and radiative dynamics in classical rela- tivistic scattering and bound systems, Phys. Rev. Res. 4, 013127 (2022), arXiv:2109.05994 [gr-qc]

    Pith/arXiv arXiv 2022

  34. [34]

    Gonzo and C

    R. Gonzo and C. Shi, Boundary to bound dictionary for generic Kerr orbits, Phys. Rev. D108, 084065 (2023), arXiv:2304.06066 [hep-th]

    Pith/arXiv arXiv 2023

  35. [35]

    Adamo, R

    T. Adamo, R. Gonzo, and A. Ilderton, Gravitational bound waveforms from amplitudes, JHEP05, 034, arXiv:2402.00124 [hep-th]

    Pith/arXiv arXiv

  36. [36]

    Khalaf, C.-H

    M. Khalaf, C.-H. Shen, and O. Telem, Bound-unbound universality and the all-order semi-classical wave function in Schwarzschild, JHEP10, 063, arXiv:2503.23317 [gr- qc]

    Pith/arXiv arXiv

  37. [37]

    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]

    Pith/arXiv arXiv 2023

  38. [38]

    Rettegno, G

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

    Pith/arXiv arXiv 2023

  39. [39]

    O. Long, C. Whittall, and L. Barack, Black hole scatter- ing near the transition to plunge: Self-force and resum- mation of post-Minkowskian theory, Phys. Rev. D110, 044039 (2024), arXiv:2406.08363 [gr-qc]

    arXiv 2024

  40. [40]

    Herrmann, J

    E. Herrmann, J. Parra-Martinez, M. S. Ruf, and M. Zeng, Radiative classical gravitational observables atO(G 3) from scattering amplitudes, JHEP10, 148, arXiv:2104.03957 [hep-th]

    Pith/arXiv arXiv

  41. [41]

    Herrmann, J

    E. Herrmann, J. Parra-Martinez, M. S. Ruf, and M. Zeng, Gravitational Bremsstrahlung from Reverse Unitarity, Phys. Rev. Lett.126, 201602 (2021), arXiv:2101.07255 [hep-th]

    Pith/arXiv arXiv 2021

  42. [42]

    M. M. Riva and F. Vernizzi, Radiated momentum in the post-Minkowskian worldline approach via reverse unitar- ity, JHEP11, 228, arXiv:2110.10140 [hep-th]

    Pith/arXiv arXiv

  43. [43]

    Di Vecchia, C

    P. Di Vecchia, C. Heissenberg, R. Russo, and G. Veneziano, Classical gravitational observables from the Eikonal operator, Phys. Lett. B843, 138049 (2023), arXiv:2210.12118 [hep-th]

    Pith/arXiv arXiv 2023

  44. [44]

    Dlapa, G

    C. Dlapa, G. K¨ alin, Z. Liu, J. Neef, and R. A. Porto, Radiation Reaction and Gravitational Waves at Fourth Post-Minkowskian Order, Phys. Rev. Lett.130, 101401 (2023), arXiv:2210.05541 [hep-th]

    Pith/arXiv arXiv 2023

  45. [45]

    P. H. Damgaard, E. R. Hansen, L. Plant´ e, and P. Van- hove, Classical observables from the exponential repre- sentation of the gravitational S-matrix, JHEP09, 183, arXiv:2307.04746 [hep-th]

    Pith/arXiv arXiv

  46. [46]

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

    Pith/arXiv arXiv 2023

  47. [47]

    W. D. Goldberger and I. Z. Rothstein, Horizon radiation reaction forces, JHEP10, 026, arXiv:2007.00731 [hep-th]

    Pith/arXiv arXiv 2007

  48. [48]

    C. R. T. Jones and M. S. Ruf, Absorptive effects and classical black hole scattering, JHEP03, 015, arXiv:2310.00069 [hep-th]

    Pith/arXiv arXiv

  49. [49]

    Cipriani, F

    A. Cipriani, F. Fucito, C. Heissenberg, J. F. Morales, and R. Russo, ”Waveforms” at the Horizon, (2026), arXiv:2602.05766 [gr-qc]

    Pith/arXiv arXiv 2026

  50. [50]

    Cutler, D

    C. Cutler, D. Kennefick, and E. Poisson, Gravita- tional radiation reaction for bound motion around a schwarzschild black hole, Phys. Rev. D50, 3816 (1994)

    1994

  51. [51]

    Glampedakis and D

    K. Glampedakis and D. Kennefick, Zoom and whirl: Ec- centric equatorial orbits around spinning black holes and their evolution under gravitational radiation reaction, Phys. Rev. D66, 044002 (2002), arXiv:gr-qc/0203086

    Pith/arXiv arXiv 2002

  52. [52]

    Gundlach, S

    C. Gundlach, S. Akcay, L. Barack, and A. Nagar, Criti- cal phenomena at the threshold of immediate merger in binary black hole systems: the extreme mass ratio case, Phys. Rev. D86, 084022 (2012), arXiv:1207.5167 [gr-qc]

    Pith/arXiv arXiv 2012

  53. [53]

    Berti, V

    E. Berti, V. Cardoso, T. Hinderer, M. Lemos, F. Pre- torius, U. Sperhake, and N. Yunes, Semianalytical esti- mates of scattering thresholds and gravitational radia- tion in ultrarelativistic black hole encounters, Phys. Rev. D81, 104048 (2010), arXiv:1003.0812 [gr-qc]

    Pith/arXiv arXiv 2010

  54. [54]

    Barausse, E

    E. Barausse, E. Berti, V. Cardoso, S. A. Hughes, and G. Khanna, Divergences in gravitational-wave emission and absorption from extreme mass ratio binaries, Phys. Rev. D104, 064031 (2021), arXiv:2106.09721 [gr-qc]

    Pith/arXiv arXiv 2021

  55. [55]

    N. Warburton, Gravitational radiation from hyper- bolic orbits: comparison between self-force, post- Minkowskian, post-Newtonian, and numerical relativity results, (2025), arXiv:2512.02274 [gr-qc]

    Pith/arXiv arXiv 2025

  56. [56]

    Barack, M

    L. Barack, M. Colleoni, T. Damour, S. Isoyama, and N. Sago, Self-force effects on the marginally bound zoom- whirl orbit in Schwarzschild spacetime, Phys. Rev. D 100, 124015 (2019), arXiv:1909.06103 [gr-qc]

    Pith/arXiv arXiv 2019

  57. [57]

    Gonzo, J

    R. Gonzo, J. Lewis, and A. Pound, The first law of binary black hole scattering, (2024), arXiv:2409.03437 [gr-qc]

    arXiv 2024

  58. [58]

    Parnachev and K

    A. Parnachev and K. Sen, Notes on AdS-Schwarzschild eikonal phase, JHEP03, 289, arXiv:2011.06920 [hep-th]

    Pith/arXiv arXiv 2011

  59. [59]

    Akpinar, V

    D. Akpinar, V. del Duca, and R. Gonzo, The spin- ning self-force EFT: 1SF waveform recursion relation and Compton scattering, (2025), arXiv:2504.02025 [hep-th]

    arXiv 2025

  60. [60]

    Damour and G

    T. Damour and G. Schaefer, Higher Order Relativistic Periastron Advances and Binary Pulsars, Nuovo Cim. B 101, 127 (1988)

    1988

  61. [61]

    Pretorius and D

    F. Pretorius and D. Khurana, Black hole mergers and un- stable circular orbits, Class. Quant. Grav.24, S83 (2007), arXiv:gr-qc/0702084

    Pith/arXiv arXiv 2007

  62. [62]

    Akcay, L

    S. Akcay, L. Barack, T. Damour, and N. Sago, Gravi- tational self-force and the effective-one-body formalism between the innermost stable circular orbit and the light ring, Phys. Rev. D86, 104041 (2012), arXiv:1209.0964 [gr-qc]

    Pith/arXiv arXiv 2012

  63. [63]

    T. C. Quinn and R. M. Wald, Energy conservation for point particles undergoing radiation reaction, Phys. Rev. D60, 064009 (1999), arXiv:gr-qc/9903014

    Pith/arXiv arXiv 1999

  64. [64]

    D. V. Gal’tsov, Radiation reaction in the Kerr gravita- tional field, J. Phys. A15, 3737 (1982)

    1982

  65. [65]

    Leather, Gravitational self-force with hyperboloidal slicing and spectral methods, Gen

    B. Leather, Gravitational self-force with hyperboloidal slicing and spectral methods, Gen. Rel. Grav.57, 112 (2025), arXiv:2411.14976 [gr-qc]

    arXiv 2025

  66. [66]

    Barack, R

    L. Barack, R. Gonzo, B. Leather, O. Long, and N. Warburton, UnstableCircularOrbitFluxes.dat, Zen- odo (2026)

    2026

  67. [67]

    Tanaka, H

    T. Tanaka, H. Tagoshi, and M. Sasaki, Gravita- tional waves by a particle in circular orbits around a Schwarzschild black hole: 5.5 postNewtonian for- mula, Prog. Theor. Phys.96, 1087 (1996), arXiv:gr- qc/9701050. 15

    arXiv 1996

  68. [68]

    Fujita, Gravitational Waves from a Particle in Cir- cular Orbits around a Schwarzschild Black Hole to the 22nd Post-Newtonian Order, Prog

    R. Fujita, Gravitational Waves from a Particle in Cir- cular Orbits around a Schwarzschild Black Hole to the 22nd Post-Newtonian Order, Prog. Theor. Phys.128, 971 (2012), arXiv:1211.5535 [gr-qc]

    Pith/arXiv arXiv 2012

  69. [69]

    Poisson and M

    E. Poisson and M. Sasaki, Gravitational radiation from a particle in circular orbit around a black hole. 5: Black hole absorption and tail corrections, Phys. Rev. D51, 5753 (1995), arXiv:gr-qc/9412027

    Pith/arXiv arXiv 1995

  70. [70]

    Fujita, Gravitational Waves from a Particle in Cir- cular Orbits around a Rotating Black Hole to the 11th Post-Newtonian Order, PTEP2015, 033E01 (2015), arXiv:1412.5689 [gr-qc]

    R. Fujita, Gravitational Waves from a Particle in Cir- cular Orbits around a Rotating Black Hole to the 11th Post-Newtonian Order, PTEP2015, 033E01 (2015), arXiv:1412.5689 [gr-qc]

    Pith/arXiv arXiv 2015

  71. [71]

    Cipriani, G

    A. Cipriani, G. Di Russo, F. Fucito, J. F. Morales, H. Poghosyan, and R. Poghossian, Resumming Post- Minkowskian and Post-Newtonian gravitational wave- form expansions, (2025), arXiv:2501.19257 [gr-qc]

    Pith/arXiv arXiv 2025

  72. [72]

    J. S. Schwinger, Brownian motion of a quantum oscilla- tor, J. Math. Phys.2, 407 (1961)

    1961

  73. [73]

    L. V. Keldysh, Diagram Technique for Nonequilibrium Processes, Sov. Phys. JETP20, 1018 (1965)

    1965

  74. [74]

    W. D. Goldberger and I. Z. Rothstein, An Effective field theory of gravity for extended objects, Phys. Rev. D73, 104029 (2006), arXiv:hep-th/0409156

    Pith/arXiv arXiv 2006

  75. [75]

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

    Pith/arXiv arXiv

  76. [76]

    W. D. Goldberger and I. Z. Rothstein, Dissipative effects in the worldline approach to black hole dynamics, Phys. Rev. D73, 104030 (2006), arXiv:hep-th/0511133

    Pith/arXiv arXiv 2006

  77. [77]

    Barack, R

    L. Barack, R. Gonzo, B. Leather, O. Long, and N. War- burton, ancillary.m, Zenodo (2026)

    2026

  78. [78]

    Blanchet and T

    L. Blanchet and T. Damour, Hereditary effects in gravi- tational radiation, Phys. Rev. D46, 4304 (1992)

    1992

  79. [79]

    R. O. Hansen, Post-Newtonian gravitational radiation from point masses in a hyperbolic kepler orbit, Phys. Rev. D5, 1021 (1972)

    1972

  80. [80]

    Turner, Gravitational radiation from point-masses in unbound orbits: Newtonian results., Astrophys

    M. Turner, Gravitational radiation from point-masses in unbound orbits: Newtonian results., Astrophys. J.216, 610 (1977)

    1977

Showing first 80 references.