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REVIEW 3 major objections 5 minor 31 references

Radiation-reaction driven dynamics at the third-and-a-half post-Newtonian order in different gauges

T0 review · 3 major / 5 minor · reviewed 2026-08-12 · deepseek-v4-flash

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Pith's one-line read At 3.5PN order, radiation-reaction dynamics can be moved between coordinate systems by coordinate transformation alone, without re-solving the balance equations.

desk verdict A useful and mostly solid 3.5PN map between harmonic and ADM/EOB radiation-reaction forces, but the 'coordinate-only' framing oversells a gauge-dependent and partially unproven recipe. read the letter →

arxiv 2608.10965 v1 pith:4MESNOPW submitted 2026-08-11 gr-qc

Donato Bini , Andrea Geralico , Sara Rufrano Aliberti This is my paper · ORCID
classification gr-qc PACS 04.25.Nx04.30.-w
keywords radiationreactionpost-Newtonianexpansion3.5PNordergaugedependenceharmoniccoordinatesADMeffectiveonebodySchottterms
verification ladder T0 review T1 audit T2 compute T3 formal

The pith

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

The reading

This paper claims that at the third-and-a-half post-Newtonian order, the radiation-reaction force, the Schott terms, and the radiation-reaction correction to the orbit in any Hamiltonian coordinate system can be obtained from the known harmonic-coordinate results by coordinate transformation alone, without re-solving the balance equations. The argument identifies the harmonic-coordinate mechanical energy and angular-momentum loss rates with the combination $\dot r F_r + \dot\phi F_\phi$ and the component $F_\phi$ in the new phase-space variables, leaving all residual gauge freedom in a set of unspecified gauge parameters. Explicit maps from modified harmonic coordinates to Arnowitt-Deser-Misner (ADM) and to Effective-One-Body (EOB) phase-space coordinates are constructed through $O(\eta^7)$, and the transformed force components and Schott terms are displayed with gauge parameters left free. If the construction is correct, it turns gauge translation into an algebraic step, which matters because EOB waveform models rely on several different gauge choices and previously needed a fresh solution of the radiation-reacted dynamics for each.

What carries the argument

The load-bearing mechanism is the PN-expanded coordinate and momentum map from modified harmonic coordinates to the target Hamiltonian frame, $r_h = f_r(r, \phi, p_r, L)$, $\phi_h = f_\phi(r, \phi, p_r, L)$, together with the energy-loss identification Eq. (3.21). The map's coefficients are fixed order by order by requiring that the accelerations computed from Poisson brackets in the new variables reproduce the known modified-harmonic acceleration, including the radiation-reaction part with unspecified gauge parameters; with the map in hand, the harmonic-coordinate balance results are transported to the new gauge, and its inverse converts the harmonic orbit solution to the new coordinates.

What would settle it

Take a specific EOB gauge choice, integrate the EOB equations of motion with the paper's transformed $F_r$ and $F_\phi$ for an eccentric orbit, and compare the evolved $r(t)$ and $\phi(t)$ against the orbit obtained by inverting the coordinate map on the known harmonic solution; any difference at $O(\eta^7)$ beyond numerical error would show that the map or the force identification is incomplete.

Watch

Extended reading notes

Core claim

On its own terms, the paper's central discovery is that the coordinate-dependent parts of the 3.5PN radiation-reaction problem are already contained in the harmonic-coordinate solution: once the losses $\partial E_{\rm cons}/\partial v^i\, a^i_{\rm rr}$ and $\partial J_{\rm cons}/\partial v^i\, a^i_{\rm rr}$ are identified with $\dot r F_r + \dot\phi F_\phi$ and $F_\phi$ in a new Hamiltonian frame, Eq. (3.21), only the coordinate mapping between harmonic variables and the new phase-space variables is needed to determine the radiation-reaction force and Schott terms. The paper derives that mapping for ADM and EOB coordinates to 3.5PN order, including radiation-reaction terms in the map itself, and uses its inverse to convert the known harmonic-coordinate radiation-reacted orbit into the corresponding orbit in the new coordinates, avoiding the coupled differential equations of the variation-of-constants method.

Load-bearing premise

The construction rests on the assumption that the harmonic-coordinate mechanical energy and angular-momentum loss rates translate exactly into $\dot r F_r + \dot\phi F_\phi$ and $F_\phi$ in the new Hamiltonian frame, with any ambiguity absorbed into Schott terms, and that the polynomial coordinate-map ansatz contains every term needed at 3.5PN order in the new gauge.

Editorial extensions

If this is right

  • For ADM coordinates, where all gauge parameters are already fixed, the paper gives complete explicit expressions for the 3.5PN radiation-reaction force, Schott energy, and Schott angular momentum in Hamiltonian phase-space variables.
  • For EOB coordinates, the same prescription yields force and Schott terms as functions of the free gauge parameters, so recent and future gauge choices in waveform models can be compared and substituted without recomputing balance equations.
  • The radiation-reaction correction to the orbit in the new coordinate system is obtained by inverting the coordinate map and substituting the known harmonic solution, so no separate variational-equation solve is needed for each gauge.
  • Because only fluxes at infinity are gauge-invariant, the residual freedom is confined to the Schott terms and the force components, matching the fact that different EOB gauge choices leave observable phasing unchanged.
  • The stated generalization path to 4.5PN order and to spin corrections stays within the same scheme, since only the harmonic input and the maps would need updating.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

  • If the maps are complete, a direct numerical check is possible: integrate the EOB equations of motion with the transformed $F_r$ and $F_\phi$ for a given gauge choice and compare with the transformed harmonic orbit; agreement at $O(\eta^7)$ would confirm the reshuffling into Schott terms, and disagreement would localize missing terms in the map.
  • The construction suggests a modular workflow for waveform models: keep the harmonic-coordinate radiation-reaction engine and the gauge parameters as a separate layer from the EOB Hamiltonian, so that changing a gauge amounts to swapping a finite set of coefficients rather than re-deriving dynamics.
  • An implicit consequence is that all EOB gauge choices satisfying the balance equations and the same map must predict identical gauge-invariant phasing; differences seen in published waveform models would then be attributed to higher-order or nonlocal (tail) effects beyond 3.5PN.
  • For eccentric orbits, the transformation of $\dot\phi$ contributes at 3.5PN to the phase; the explicit EOB orbit corrections provided here make it possible to test whether the next-to-leading-order quasi-circular condition used in one of the cited gauge choices is sufficient for eccentric waveforms or whether the radial component needs additional fixing.
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Editorial analysis

A structured set of objections, weighed in public.

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

Referee Report

3 major / 5 minor

Summary. The paper presents a method for obtaining the 3.5PN radiation-reaction force and Schott terms in a Hamiltonian coordinate system (ADM or EOB) from the known harmonic-coordinate Iyer-Will balance results. The authors' central claim is that, once the harmonic-coordinate solution is known, only the coordinate transformation between harmonic coordinates and the new phase-space variables is needed, without re-solving the balance equations. They provide explicit coordinate maps in Appendix A, expressions for the force components and Schott terms in ADM and EOB coordinates with the IW gauge parameters left free in the EOB case, reductions to several published EOB gauge choices, and formulas for the radiation-reaction correction to the orbit obtained by transforming the known harmonic-coordinate solution.

Significance. If fully substantiated, the paper would provide a convenient shortcut for translating radiation-reaction results between coordinate systems, which is directly relevant to EOB waveform models. The manuscript is valuable for its explicitness: all force components, Schott terms, and coordinate maps are given in closed form, and the EOB expressions are checked against the BD minimal gauge and the gauge choices of Refs. [20,21]. However, the advertised simplification is conditional on a number of unproven regularity and uniqueness assumptions, as detailed in the major comments; the central claim is therefore not yet established at the level claimed in the abstract.

major comments (3)
  1. [Section V.B, Eq. (3.21)] The identification in Eq. (3.21) is the load-bearing step of the method. The paper itself notes in Eq. (3.22) that this identification is exact only at leading order, and that at 3.5PN one may reshuffle contributions via Schott terms. In the EOB case, direct application of Eq. (3.21) produces 1/p_r singularities in F_r, which are removed only by manually modifying the Schott energy (Section V.B, text preceding Eq. (5.3)). The paper does not prove that for every admissible set of IW gauge parameters a regular F_r and a consistent Schott reshuffling exist. Without such an existence argument, the claim that only the coordinate transformation is needed is not a theorem but a procedure supplemented by an unstated regularity condition. The authors should either prove the existence of the reshuffling or restate the claim as conditional on this regularity requirement.
  2. [Appendix A, Eqs. (A3)-(A4)] The map from harmonic to EOB coordinates is not a fixed chart transformation: the coefficients C_1 through C_6 in Eq. (A4) depend linearly on the IW gauge parameters α, β, δ_i, and ε_5, which parametrize the arbitrary split of E* and J* into system plus Schott terms rather than the choice of coordinate chart. Hence the map absorbs exactly the balance ambiguity that the abstract claims to avoid. If the two charts were genuinely specified, a coordinate transformation would be fixed once the charts are given; here the result is a multi-parameter family of maps labeled by the balance gauge. The paper should either demonstrate that the EOB coordinate chart itself fixes these parameters (for example by an independent definition of EOB coordinates) or explicitly characterize the result as a family of maps parameterized by the IW gauge freedom. The derivation is also presented only as 'we find' in Appendix A, which makes it difficult to verify how the gauge dependence enters.
  3. [Section V.A] The ADM radiation-reaction force is not cross-checked against the independent first-principle ADM result of Refs. [5,15]. Since the ADM gauge parameters are fully determined (Table I), substituting them into Eqs. (5.1)-(5.2) should reproduce the known ADM rr force, providing a direct validation of the whole apparatus. The paper currently presents these formulas without comparison. This omission is load-bearing because the ADM case is the only one where the transformation can be tested against an independent derivation; without this comparison, the reader cannot distinguish a correct derivation from an internally consistent but incorrect mapping.
minor comments (5)
  1. [Section V.B] The phrase 'Differently form the ADM case' should read 'Differently from the ADM case'.
  2. [Section V.B.2] There is a typographical duplication in 'Eqs. Eqs. (40) and (43) in Ref. [20]'.
  3. [Section II] The notation η = 1/c as a PN expansion parameter is nonstandard and may be confused with the symmetric mass ratio ν; a brief clarification or a different symbol (e.g., ε) would improve readability.
  4. [Section VI, Eq. (6.4)] The expression for δ^{rr,G3}r_h(t) contains nested parentheses that appear unbalanced in the typeset version; the authors should verify the bracket structure.
  5. [Appendix A] The coordinate transformations are presented as final results with no derivation shown; given that these maps are central to the paper, a brief outline of the matching procedure and the number of equations solved at each PN order would be helpful.

Circularity Check

2 steps flagged · score 2.0 of 10

No significant hidden circularity: the paper is an explicit conversion rule, but the new-coordinate radiation-reaction force is by construction the transformed harmonic balance result, and the harmonic orbit input comes from the authors' prior work.

  1. self definitional [Section III.C, Eq. (3.21), and Section V.B, Eqs. (5.3)-(5.4)]
    "The components of the rr force in the new Hamiltonian coordinate system X directly follow from Eq. (3.21), where the lhs of each equation (written in harmonic coordinates) is evaluated by applying the mapping h→X derived in the previous section."

    Eq. (3.21) defines the new-coordinate force combination ˙rF_r + ˙ϕF_ϕ and F_ϕ to be, by construction, the harmonic mechanical energy and angular momentum loss rates after the h→X mapping. Consequently the listed EOB force components in Eqs. (5.3)-(5.4) are not independent predictions; they are the harmonic IW-balance result rewritten in EOB variables, and they inherit the IW gauge parameters α, β, δ_i, ϵ_5. The paper openly concedes this non-uniqueness ('Obviously Eqs. (3.21) do not provide a unique definitions for the force components...'), and it presents the result as a prescription rather than as a first-principles derivation. This is a transparent definitional construction, not a hidden circularity, but it does mean the EOB force cannot validate the balance method independently.

  2. self citation load bearing [Section VI and Ref. [24]]
    "In a previous work [24] we have computed the radiation-reaction corrected orbit in harmonic coordinates at the 3.5PN order in the case of hyperboliclike motion... One can easily verify that the above solution satisfies the equations of motion with the harmonic components (3.17) of the rr force."

    The harmonic 3.5PN radiation-reaction orbit used as the input for the coordinate-transformation step of Section VI is taken from the authors' own previous paper, Ref. [24]. This is a self-citation, and it is load-bearing for the claimed 'remarkable simplification' of obtaining the new-coordinate orbit without re-solving the dynamics. However, the harmonic solution is a prior, independently published result that the paper states can be verified against the harmonic equations of motion; it is not the target EOB or ADM claim. Thus the self-citation is an input, not a validation loop, and is only mildly relevant to circularity.

full rationale

The paper's stated aim is to give a coordinate-translation recipe for the 3.5PN radiation-reaction force, not to predict new physics. The central identification, Eq. (3.21), is explicitly definitional: the harmonic-coordinate mechanical losses are declared to equal ˙rF_r + ˙ϕF_ϕ and F_ϕ in the new Hamiltonian chart, and the subsequent EOB/ADM expressions are obtained by substituting the Appendix A maps. The paper repeatedly acknowledges the resulting non-uniqueness through the IW gauge parameters and Schott terms, so there is no disguised fit or imported uniqueness theorem. The coordinate maps themselves are fixed by matching the known harmonic accelerations order by order, with all coefficients displayed, and the gauge-parameter dependence of the maps is stated rather than hidden. The only notable self-citation is Ref. [24], the authors' prior harmonic 3.5PN orbit solution, which is used as an input to the transformation; it is checkable against the harmonic equations of motion and is not identical to the new-coordinate result being claimed. No circular step forces the central result; the paper is essentially a self-contained conversion dictionary with a mild definitional character and a minor load-bearing self-citation. Score 2 reflects that the EOB output is a transformed harmonic result rather than an independent prediction, while the paper is transparent about this and does not overclaim.

Assumptions & free parameters 8 free parameters · 4 assumptions · 0 invented entities

The method does not introduce new physical entities. It inherits the gauge parameters of the IW balance construction and relies on standard PN assumptions about balance equations, harmonic-coordinate results, and coordinate maps.

free parameters (8)
  • α (2.5PN gauge parameter) = left arbitrary in EOB; fixed in ADM by Refs [6,7]
    Gauge parameter in the IW balance construction, appears in the 2.5PN rr force and Schott terms, left free in EOB expressions.
  • β (2.5PN gauge parameter) = left arbitrary in EOB; fixed in ADM by Refs [6,7]
    Gauge parameter in the IW balance construction, appears in the 2.5PN rr force and Schott terms, left free in EOB expressions.
  • δ1 (3.5PN gauge parameter) = left arbitrary in EOB; fixed in ADM by Refs [6,7]
    3.5PN gauge parameter in the IW balance construction, enters the 3.5PN force and Schott terms.
  • δ2 (3.5PN gauge parameter) = left arbitrary in EOB; fixed in ADM by Refs [6,7]
    3.5PN gauge parameter in the IW balance construction, enters the 3.5PN force and Schott terms.
  • δ3 (3.5PN gauge parameter) = left arbitrary in EOB; fixed in ADM by Refs [6,7]
    3.5PN gauge parameter in the IW balance construction, enters the 3.5PN force and Schott terms.
  • δ4 (3.5PN gauge parameter) = left arbitrary in EOB; fixed in ADM by Refs [6,7]
    3.5PN gauge parameter in the IW balance construction, enters the 3.5PN force and Schott terms.
  • δ5 (3.5PN gauge parameter) = left arbitrary in EOB; fixed in ADM by Refs [6,7]
    3.5PN gauge parameter in the IW balance construction, enters the 3.5PN force and Schott terms.
  • ε5 (3.5PN gauge parameter) = left arbitrary in EOB; fixed in ADM by Refs [6,7]
    3.5PN gauge parameter in the IW balance construction, enters the 3.5PN force and Schott terms.
assumptions (4)
  • domain assumption Balance equations (2.12) hold with Schott terms accounting for the gauge-dependent split of energy and angular momentum losses.
    The IW balance method (Ref [13]) is assumed to be valid at 3.5PN; this underlies the entire construction of the force.
  • domain assumption The harmonic-coordinate 3.5PN radiation-reaction force and Schott terms from Refs [6,7] are correct.
    These are taken as the starting point; any error in those results propagates into the converted force.
  • ad hoc to paper The identification in Eq. (3.21) correctly maps harmonic-coordinate energy and angular momentum loss rates to the new-coordinate force components.
    This is the core methodological assumption of the paper; at 3.5PN it relies on the ability to reshuffle contributions into Schott terms.
  • domain assumption A PN-expanded coordinate transformation (4.5) exists and can be determined by matching the accelerations order by order.
    The paper assumes the ansatz for the map and that solving the resulting linear equations yields the transformation; this is standard in PN coordinate-change derivations but not proved here.

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Cite this review

Pith. "Pith review of Radiation-reaction driven dynamics at the third-and-a-half post-Newtonian order in different gauges." pith.science (2026). https://pith.science/paper/4MESNOPW

@misc{pith2026260810965,
  author       = {Pith},
  title        = {Pith review of: Radiation-reaction driven dynamics at the third-and-a-half post-Newtonian order in different gauges},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/4MESNOPW}},
  note         = {Machine review of arXiv:2608.10965}
}
read the original abstract

We consider the coordinate-dependent definition of the radiation-reaction force at the third-and-a-half post-Newtonian order for general orbits. In order to (partially) determine its expression we refer to the balance method, involving the energy and angular momentum lost by the system, the Schott terms, and the energy and angular momentum fluxes at infinity. Only the latter are gauge-invariant quantities when passing from a coordinate system to another. The gauge dependence of both radiation-reaction force and Schott terms is encoded in a set of gauge parameters entering their definitions. We show how to relate the harmonic-coordinate losses of mechanical energy and angular momentum by the system with the radial and azimuthal components of the radiation-reaction force in a different coordinate system expressed in terms of phase-space variables in a Hamiltonian framework. The advantage of this approach is that only the coordinate transformation between harmonic coordinates and coordinates and momenta in the new coordinate system is needed, without solving again the balance equations. We derive such a transformation for both Arnowitt-Deser-Misner and Effective-One-Body coordinates. In the latter case we also discuss some simplifying choices of the gauge parameters adopted in current waveform models. Finally, we show how to obtain the solution for the radiation-reaction correction to the orbit in the new coordinate system simply by transforming the harmonic-coordinate solution known in the literature. This is a remarkable simplification, since one can avoid to solve again for the radiation-reacted dynamics.

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Works this paper leans on

31 extracted references · 12 canonical work pages

  1. [22]

    Transition from inspiral to plunge in binary black hole coalescences,

    A. Buonanno and T. Damour, “Transition from inspiral to plunge in binary black hole coalescences,” Phys. Rev. D62, 064015 (2000) [arXiv:gr-qc/0001013 [gr-qc]]

    arXiv 2000

  2. [1]

    Gauge choices in Ref. [18] The BD gauge consists in imposing the conditionJ Schott ≡0, namely α= 0, δ 1 = 137 21 ν− 307 84 , δ 3 = 271 42 − 107 21 ν , ϵ 5 = 0,(5.5) so thatF ϕ =−Φ J , i.e., F rr ϕ = 8 5 η5ν2 L r3 − 2L2 r2 +p 2 r − 2 r +η 2 L4 r4 53ν 21 − 55 84 + L2p2 r r2 137ν 42 − 11 21 + L2 r3 137ν 21 + 247 21 + − 59ν 42 − 137 42 p4 r + p2 r r 16ν 3 − 2...

    work page

  3. [2]

    M. Picone,

    Gauge choices in Refs. [20–22] Refs. [20–22] have explored different gauge choices for the radiation-reaction force at the leading and next-to-leading orders, to be used in the construction of EOB-based waveform models. In Refs. [20, 21] the authors work directly in EOB coordinates. They focused on the quasi-circular case, and specify the gauge coefficien...

    work page

  4. [3]

    Probl` eme des deux corps et freinage de ray- onnement en relativit´ e g´ en´ erale,

    T. Damour; “Probl` eme des deux corps et freinage de ray- onnement en relativit´ e g´ en´ erale,” C.R. Acad. Sc. Paris, S´ erie II,294, pp 1355-1357 (1982)

    work page 1982

  5. [4]

    Harmonic to ADM The transformation between harmonic coordinates and ADM coordinates is known for the conservative part up to the 3PN order (see Ref. [26]). The rr part is new with this work. We find rh =r+η 4 − 7 4 ν p2 r r + 5 8 L2 r3 ν+ 1 4 + 3ν 1 r2 r+ 8 15 η5ν pr r +η 6 − 47 24 ν2 + 7 24 ν p4 r r + 1 16 ν2 − 5 16 ν p2 r L2 r3 + 39 8 ν2 + 53 24 ν p2 r ...

    work page

  6. [5]

    [22] (see Appendix A there)

    Harmonic to EOB The transformation between harmonic coordinates and EOB coordinates has been derived through the 3PN order in Ref. [22] (see Appendix A there). We extend it here to the 3.5PN level, so that besidesαandβit also contains 18 the six 3.5PN gauge parametersδ i,i= 1, . . . ,5, andϵ5. We find rh =r+η 2 L2ν 2r2 + 3νp2 r 2 + 1 r − ν 2 −1 r +η 4 L4 ...

    work page

  7. [6]

    Post-Newtonian Theory for Gravitational Waves,

    L. Blanchet, “Post-Newtonian Theory for Gravitational Waves,” Living Rev.Rel.27, 1, 4 (2024) [arXiv:1310.1528 [gr-qc]]

    arXiv 2024

  8. [7]

    Radiation Reaction and Angular Momentum Loss in Small Angle Gravitational Scattering,

    T. Damour and N. Deruelle, “Radiation Reaction and Angular Momentum Loss in Small Angle Gravitational Scattering,” Phys. Lett. A87, 81 (1981)

    work page 1981

Show all 31 references
  1. [8]

    Gravitational radiation reaction and bal- ance equations to post-Newtonian order,

    L. Blanchet, “Gravitational radiation reaction and bal- ance equations to post-Newtonian order,” Phys. Rev. D 55, 714-732 (1997) [arXiv:gr-qc/9609049 [gr-qc]]

    1997 arXiv

  2. [9]

    Gravitational radiation reaction in the bi- nary pulsar and the quadrupole formula controversy,

    T. Damour, “Gravitational radiation reaction in the bi- nary pulsar and the quadrupole formula controversy,” Phys. Rev. Lett.51, 1019-1021 (1983)

    1983

  3. [10]

    Radiative 3.5 post- Newtonian ADM Hamiltonian for many body point - 20 mass systems,

    P. Jaranowski and G. Schaefer, “Radiative 3.5 post- Newtonian ADM Hamiltonian for many body point - 20 mass systems,” Phys. Rev. D55, 4712-4722 (1997)

    1997

  4. [11]

    M. E. Pati and C. M. Will, “Post-Newtonian gravita- tional radiation and equations of motion via direct in- tegration of the relaxed Einstein equations. 2. Two-body equations of motion to second post-Newtonian order, and radiation reaction to 3.5 post-Newtonian order,” Phys. R...

    2002 arXiv

  5. [12]

    Gravitational radiation reaction in the equations of motion of compact binaries to 3.5 post-Newtonian order,

    S. Nissanke and L. Blanchet, “Gravitational radiation reaction in the equations of motion of compact binaries to 3.5 post-Newtonian order,” Class. Quant. Grav.22, 1007-1032 (2005) [arXiv:gr-qc/0412018 [gr-qc]]

    2005 arXiv

  6. [13]

    Post-Newtonian gravitational radiation reaction for two-body systems: Nonspinning bodies,

    B. R. Iyer and C. M. Will, “Post-Newtonian gravitational radiation reaction for two-body systems: Nonspinning bodies,” Phys. Rev. D52, 6882 (1995)

    1995

  7. [14]

    Gravitational radi- ation reaction for compact binary systems at the fourth- and-a-half post-Newtonian order,

    L. Blanchet, G. Faye and D. Trestini, “Gravitational radi- ation reaction for compact binary systems at the fourth- and-a-half post-Newtonian order,” Class. Quant. Grav. 42, no.6, 065015 (2025) [arXiv:2407.18295 [gr-qc]]

    2025 arXiv

  8. [15]

    Gravi- tational radiation reaction for compact binary systems at the fourth-and-a-half post-Newtonian order in harmonic coordinates,

    L. Blanchet, G. Faye, E. Seraille and D. Trestini, “Gravi- tational radiation reaction for compact binary systems at the fourth-and-a-half post-Newtonian order in harmonic coordinates,” Class. Quant. Grav.43, no.10, 105009 (2026) [arXiv:2601.06743 [gr-qc]]

    2026 arXiv

  9. [16]

    Radiation reaction at 3.5 post-Newtonian order in effective field theory,

    C. R. Galley and A. K. Leibovich, “Radiation reaction at 3.5 post-Newtonian order in effective field theory,” Phys. Rev. D86, 044029 (2012) [arXiv:1205.3842 [gr-qc]]

    2012 arXiv

  10. [17]

    Radiation reaction for nonspinning bodies at 4.5PN in the effective field theory approach,

    A. K. Leibovich, B. A. Pardo and Z. Yang, “Radiation reaction for nonspinning bodies at 4.5PN in the effective field theory approach,” Phys. Rev. D108, no.2, 024017 (2023) [arXiv:2302.11016 [gr-qc]]

    2023 arXiv

  11. [18]

    Gravitational radiation reac- tion along general orbits in the effective one-body formal- ism,

    D. Bini and T. Damour, “Gravitational radiation reac- tion along general orbits in the effective one-body formal- ism,” Phys. Rev. D86, 124012 (2012) [arXiv:1210.2834 [gr-qc]]

    2012 arXiv

  12. [19]

    Time asymmetric structure of gravitational radiation,

    L. Blanchet, “Time asymmetric structure of gravitational radiation,” Phys. Rev. D47, 4392-4420 (1993)

    1993

  13. [20]

    The Binary black hole dynamics at the third-and-a-half postNewto- nian order in the ADM formalism,

    C. Konigsdorffer, G. Faye and G. Schaefer, “The Binary black hole dynamics at the third-and-a-half postNewto- nian order in the ADM formalism,” Phys. Rev. D68, 044004 (2003) [arXiv:gr-qc/0305048 [gr-qc]]

    2003 arXiv

  14. [21]

    Effective one-body ap- proach to general relativistic two-body dynamics,

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

    1999 arXiv

  15. [23]

    Phasing of gravitational waves from inspiralling eccentric binaries,

    T. Damour, A. Gopakumar and B. R. Iyer, “Phasing of gravitational waves from inspiralling eccentric binaries,” Phys. Rev. D70, 064028 (2004) [arXiv:gr-qc/0404128 [gr-qc]]

    2004 arXiv

  16. [24]

    Second post- Newtonian gravitational radiation reaction for two-body systems: Nonspinning bodies,

    A. Gopakumar, B. R. Iyer and S. Iyer, “Second post- Newtonian gravitational radiation reaction for two-body systems: Nonspinning bodies,” Phys. Rev. D55, 6030- 6053 (1997) [erratum: Phys. Rev. D57, 6562 (1998)] [arXiv:gr-qc/9703075 [gr-qc]]

    1997 arXiv

  17. [25]

    by including radiation reaction. The starting point is the Hamiltonian description re- called above, which can be equivalently summarized by the following evolution equations ˙r={r, H}= ∂H ∂pr , ˙ϕ={ϕ, H}= ∂H ∂pϕ , ˙pr ={p r, H}+Fr =− ∂H ∂r +F r , ˙pϕ ={p ϕ, H}+Fϕ =− ∂H ∂ϕ +F ...

  18. [26]

    Radiation-reaction force and multipolar waveforms for eccentric, spin-aligned binaries in the effective-one-body formalism,

    M. Khalil, A. Buonanno, J. Steinhoff and J. Vines, “Radiation-reaction force and multipolar waveforms for eccentric, spin-aligned binaries in the effective-one-body formalism,” Phys. Rev. D104, no.2, 024046 (2021) [arXiv:2104.11705 [gr-qc]]

    2021 arXiv

  19. [27]

    Effective-one-body multipolar waveforms for ec- centric binary black holes with nonprecessing spins,

    A. Ramos-Buades, A. Buonanno, M. Khalil and S. Os- sokine, “Effective-one-body multipolar waveforms for ec- centric binary black holes with nonprecessing spins,” Phys. Rev. D105, no.4, 044035 (2022) [arXiv:2112.06952 [gr-qc]]

    2022 arXiv

  20. [28]

    Third post- Newtonian dynamics for eccentric orbits and aligned spins in the effective-one-body waveform model seob- nrv5ehm,

    A. Gamboa, M. Khalil and A. Buonanno, “Third post- Newtonian dynamics for eccentric orbits and aligned spins in the effective-one-body waveform model seob- nrv5ehm,” Phys. Rev. D112, no.4, 044037 (2025) [arXiv:2412.12831 [gr-qc]]

    2025 arXiv

  21. [29]

    Radiation- reaction correction to scattering binary dynamics at the next-to-leading post-Newtonian order,

    D. Bini, A. Geralico and S. Rufrano Aliberti, “Radiation- reaction correction to scattering binary dynamics at the next-to-leading post-Newtonian order,” Phys. Rev. D 112, no.10, 104005 (2025) [arXiv:2509.17853 [gr-qc]]

    2025

  22. [30]

    Equivalence between the ADM-Hamiltonian and the harmonic coordi- nates approaches to the third postNewtonian dynamics of compact binaries,

    T. Damour, P. Jaranowski and G. Schaefer, “Equivalence between the ADM-Hamiltonian and the harmonic coordi- nates approaches to the third postNewtonian dynamics of compact binaries,” Phys. Rev. D63, 044021 (2001) [erratum: Phys. Rev. D66, 029901 (2002)] [arXiv:gr- qc/0010040 [gr-qc]]

    2001

  23. [31]

    Third postNewtonian dy- namics of compact binaries: Equations of motion in the center-of-mass frame,

    L. Blanchet and B. R. Iyer, “Third postNewtonian dy- namics of compact binaries: Equations of motion in the center-of-mass frame,” Class. Quant. Grav.20, 755 (2003) [arXiv:gr-qc/0209089 [gr-qc]]

    2003 arXiv

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