Pith. sign in

REVIEW 2 major objections 4 minor 83 references

Quasi-Keplerian parametrization for compact binaries on hyperbolic orbits in scalar-tensor theories at second post-Newtonian order

T0 review · 2 major / 4 minor · reviewed 2026-08-16 · deepseek-v4-flash

Challenge this review Re-run · record.json Download PDF Read on arXiv ↗ Review JSON

Pith's one-line read Massless scalar-tensor binaries on hyperbolic orbits now have a complete analytic scattering angle through 2.5 post-Newtonian order, with the conservative part from a new 2PN quasi-Keplerian parametrization and the dissipative part from…

desk verdict Solid PN calculation with a plausible but under-verified dissipative completion; deserves review, with conditions. read the letter →

arxiv 2504.13829 v2 pith:4ABYNFVG submitted 2025-04-18 gr-qc

Davide Usseglio , David Trestini , Abhishek Chowdhuri This is my paper · ORCID
classification gr-qc PACS 04.30.-w04.25.Nx04.50.Kd
keywords scalar-tensortheoriesquasi-Keplerianparametrizationhyperbolicorbitspost-Newtonianexpansionscatteringanglegravitationalradiationfluxbalanceimpactparameter
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

The paper claims that the two-body scattering problem for compact binaries in massless scalar-tensor theories is now analytically complete to 2.5 post-Newtonian (PN) order. It establishes the hyperbolic quasi-Keplerian parametrization at 2PN, giving the conservative scattering angle and impact parameter, and it supplies the dissipative corrections from scalar and gravitational radiation at 1.5PN and 2.5PN. The results include the total energy and angular momentum losses, the parabolic and bremsstrahlung limits, and a seventh post-Minkowskian re-expansion. If correct, this provides the first full 2.5PN scattering angle beyond general relativity in this theory class, and it corrects the 3PN general-relativistic impact parameter used in earlier work.

What carries the argument

The carrier is the hyperbolic quasi-Keplerian parametrization: $r = \bar a_r(\bar e_r \cosh \bar u - 1)$, a generalized Kepler equation $\bar n(t-t_0) = \bar e_t \sinh \bar u - \bar u + \bar g_t \bar v + \bar f_t \sin \bar v$, and an angular equation $\phi/\bar K = \bar v + \bar f_\phi \sin 2\bar v + \bar g_\phi \sin 3\bar v$, with hyperbolic eccentric anomaly $\bar u$ and true anomaly $\bar v$. All parameters are built from the coefficients $A,B,C,D_i,I_i$ of the radial polynomial $R(s)$ and angular series $S(s)$ in the equations of motion, so the same construction specializes to general relativity or to scalar-tensor theories. The dissipative scattering angle is obtained via the linear response rule $\chi_{\rm diss} = \frac12(\partial\chi_{\rm cons}/\partial E \,\Delta E + \partial\chi_{\rm cons}/\partial J \,\Delta J)$, with $\Delta E$ and $\Delta J$ computed by integrating the Newtonian-order fluxes over the unbound orbit.

What would settle it

Compute the 2.5PN dissipative scattering angle for a massless scalar-tensor hyperbolic encounter by direct integration of the 2.5PN equations of motion with the scalar and tensor radiation-reaction terms, bypassing the linear-response formula, and compare the result with Eq. (5.5); any disagreement at the claimed 2.5PN order would refute the completion.

Watch

Extended reading notes

Core claim

The paper establishes that, for massless scalar-tensor theories, unbound two-body motion admits a 2PN-accurate quasi-Keplerian parametrization with hyperbolic radial, Kepler, and angular equations, and that this parametrization is enough to compute all conservative observables. Combining it with flux-balance and a linear-response formula for radiation reaction, the total scattering angle is completed to 2.5PN, joining conservative and dissipative contributions. The paper also shows that the 2PN conservative scattering angle obeys the scatter-to-bound map with the periastron advance, and that in general relativity the 3PN impact parameter differs from previously published values.

Load-bearing premise

The 2.5PN dissipative scattering angle assumes the radiation-reaction force in the scalar sector is time-antisymmetric at the required order — a property proven in general relativity and asserted here to carry over to scalar-tensor theories without an independent check; if that fails, the dissipative completion breaks down.

Editorial extensions

If this is right

  • The 2PN conservative scattering angle and impact parameter become available benchmarks for future post-Minkowskian scattering calculations in scalar-tensor theories.
  • The 2.5PN complete scattering angle provides the first dissipative corrections beyond general relativity at this order, allowing quantitative tests of how scalar dipole radiation alters hyperbolic encounters.
  • The corrected 3PN general-relativistic impact parameter should replace the expressions in earlier hyperbolic-orbit waveform papers that inherit the previous value.
  • The parabolic-limit results connect hyperbolic losses to bound-orbit fluxes, supplying a boundary condition for future bound-unbound maps that include radiation.
  • The seventh post-Minkowskian re-expansion of the energy and angular momentum losses gives explicit coefficients that independent PM computations can check.

Reading between the lines

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

  • A natural next step is to derive the 3PN dissipative scattering angle in scalar-tensor theories once the hereditary scalar tails and radiation-reaction-squared terms are computed; the paper explicitly identifies these as the blocking orders.
  • Because the construction relies only on the generic polynomial form of the equations of motion, it should extend to any local-in-time alternative theory whose 2PN dynamics fit that form, not only to massless scalar-tensor theories.
  • The strong scalar dipole emission for unequal-mass systems suggests the 2.5PN dissipative corrections in scalar-tensor theories can differ substantially from the general-relativistic baseline, a difference that a future PM calculation could quantify.
  • If the corrected 3PN general-relativistic impact parameter propagates into downstream GR hyperbolic waveform models, previously published 3PN waveform results may need revision in their impact-parameter dependence.
Share X Bluesky LinkedIn Reddit HN

Signed reviews

No signed human review yet.

Editorial analysis

A structured set of objections, weighed in public.

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

Referee Report

2 major / 4 minor

Summary. The paper extends the quasi-Keplerian parametrization for compact binaries on hyperbolic orbits to massless scalar-tensor (ST) theories at second post-Newtonian (2PN) order, building on the authors' earlier quasielliptic work. From this parametrization it computes the conservative scattering angle and impact parameter, verifies the scatter-to-bound map, computes total radiated energy and angular momentum, studies parabolic and bremsstrahlung limits, and uses flux-balance and linear-response arguments to obtain dissipative corrections to the scattering angle at 1.5PN and 2.5PN. The paper claims completion of the full scattering angle at 2.5PN in these theories and also presents a corrected 3PN expression for the conservative impact parameter in general relativity.

Significance. If the results hold, they would constitute a substantial advance: the first hyperbolic-orbit quasi-Keplerian parametrization in ST theories at 2PN, a conservative scattering angle consistent with the bound-state map, and a complete 2.5PN scattering angle including dissipative effects. The paper is careful and includes several nontrivial checks: agreement with the GR quasi-Keplerian parametrization in the GR limit, agreement with the conservative ST scattering angle of Ref. [58] after correcting a typo there, agreement of the parabolic limit of the energy loss with the quasielliptic flux, and the scatter-to-bound map. The machine-readable supplemental material is a practical strength.

major comments (2)
  1. [Section V, Eq. (5.3) and following paragraph] The formula χ_diss = (1/2)(∂χ_cons/∂E ΔE + ∂χ_cons/∂J ΔJ) was established in GR under the explicit condition that the radiation-reaction force is time-antisymmetric. The paper states that "these arguments immediately translate to ST theories," but it provides neither a derivation for the scalar-tensor case nor an independent test of the resulting dissipative coefficients. Since Eq. (5.4) presents χ_diss as part of the claimed complete 2.5PN scattering angle, this transfer is load-bearing. The authors should either prove time-antisymmetry of the ST radiation-reaction force at the required order (including the scalar dipole sector, which is absent in GR) or validate χ_diss against an independent calculation, for instance by direct integration of the equations of motion with radiation reaction.
  2. [Eq. (5.5) and Appendix C] The prefactor m in Eq. (5.5) carries a dimension of mass, while χ_diss is a dimensionless angle. The same issue appears in the expressions for Δe_t, Δb, and Δv∞ in Appendix C, where the prefactors appear dimensionful. This points to a missing factor or a systematic notation error. As written, Eq. (5.5), which is the principal new result of Section V, is dimensionally inconsistent. Please verify all printed formulas against the Supplemental Material and correct the paper accordingly.
minor comments (4)
  1. [Section III B 2] The statement that Eq. (3.9) "even holds at 3PN in GR" is supported by the structure of the quasi-Keplerian parametrization and by coordinate checks; please explain explicitly why the fifth-order polynomial structure of R(s) and S(s) at 3PN in GR guarantees this property.
  2. [Appendix D] Since the paper corrects previous literature for the 3PN impact parameter, it would be helpful to pinpoint the step in Refs. [16] or [18, 63] where the error entered, rather than only reporting the disagreement.
  3. [Section V, paragraph after Eq. (5.3)] The sentence saying the extra Δcϕ contribution "will only enter at the order of radiation reaction squared, namely, 3PN" should clarify the PN counting, because in ST theories 3PN is also the order at which scalar tails first appear, which could be confusing.
  4. [Eq. (4.3)] The variable x with a bar is defined just before Eq. (4.3) but is easy to confuse with the relative separation vector x; consider using a different symbol such as y or ζ.

Circularity Check

0 steps flagged · score 2.0 of 10

No circular derivation found; the hyperbolic QK construction and 2.5PN dissipative angle are independent outputs, with only a minor reliance on the authors' earlier quasielliptic results and one asserted (not circular) transfer of the GR radiation-reaction formula to scalar-tensor theories.

full rationale

Walking the derivation chain: the hyperbolic QK parametrization is derived from the generic radial and angular polynomials R(s), S(s) in Eqs. (3.2)-(3.3), solved with the master integrals of Appendix A. The ST coefficients A, B, C, ... are taken from the authors' earlier quasielliptic work [56]; this is an input substitution, not a renamed prediction. The new unbound QK parameters, Eq. (3.6), and the 2PN conservative scattering angle, Eq. (3.7)/Eq. (B1l), are derived from the equations of motion and are benchmarked against independent results: GR [20,73] and ST [58]. The impact parameter follows from its definition, Eq. (3.8), as b = F/sqrt(A), and the 3PN GR version is additionally checked against the gauge-invariant definition b = J/p_cm from [21,74,75]; the disagreement with [16] is a substantive correctness claim, not a circular step. The energy and angular momentum losses, Eqs. (4.6), are evaluated from published ST flux and source-moment expressions [49,50,56] and integrated over the hyperbolic motion; the parabolic and bremsstrahlung limits in Sec. VI are limits of those integrals, not fitted outputs. The dissipative corrections in Sec. V use the linear-response formula, Eq. (5.1), which in GR follows from the time-antisymmetry of the radiation-reaction force. Section V states that these arguments 'immediately translate to ST theories' but gives no derivation; this is the main load-bearing assumption in the 2.5PN completion. It is flagged here as an unverified transfer rather than circularity: the formula is imported from external GR work [21,73,77], and it is not shown to equal any input of this paper. The paper itself honestly lists the reasons why the full 3PN scattering angle cannot yet be claimed. No parameter is fitted to the target observables, and no uniqueness theorem or ansatz is smuggled in through self-citation. The only mild concern is the use of prior results by one of the authors for the ST coefficients and fluxes; this is normal input use, not self-justification. The central hyperbolic and dissipative outputs are therefore independent, and the circularity score is low.

Assumptions & free parameters 0 free parameters · 6 assumptions · 0 invented entities

The central claim is an analytic extension of established PN machinery; no data are fitted and no new physical entities are introduced. The ST parameters (zeta, beta, gamma, delta, chi) and sensitivities are inputs from the theory and from Ref. [56], not free parameters fit to data. The assumptions listed are stated or standard within the PN-MPM framework; the main caveat is the unproven translation of GR radiation-reaction formulas to ST and the gauge-invariance claim for the impact parameter definition at 3PN.

assumptions (6)
  • domain assumption Action (2.1) defines the theory class: a single massless scalar field minimally coupled in Jordan frame, with Eardley point masses whose masses depend on the scalar field.
    All results are restricted to this class of massless scalar-tensor theories; the sensitivities and coupling derivatives are inputs from the theory and are not derived in this paper.
  • domain assumption Equations of motion for the relative separation take the polynomial form (3.3) at 2PN, with coefficients A,B,C,D_i,F,I_i of prescribed PN order and no logarithmic or nonlocal terms.
    This structure is true in ST theories at 2PN but fails at 3PN when tails appear; the entire quasi-Keplerian construction depends on it.
  • domain assumption Radiative multipole moments are identified with source moments at linear order, Eqs. (2.10)-(2.12), dropping O(1/c^3) tails and memory terms.
    The energy and angular momentum losses are computed at this linear order; nonlinear tail corrections are excluded from the present calculation.
  • domain assumption The impact parameter is given by Eq. (3.8) and equals J/p_cm via Eq. (3.10), and at 3PN in GR b = F/sqrt(A) remains valid.
    The corrected 3PN impact parameter in Appendix D rests on this gauge-invariance assumption, checked in two coordinate systems but not proven in the text.
  • domain assumption Dissipative evolution of QK parameters follows the linear-response formula (5.1), and the dissipative scattering angle is half the linear-response shift, Eq. (5.3), relying on time-antisymmetry of the radiation-reaction force.
    These results are established in GR; the paper assumes they carry over to ST theories at the orders needed for the 2.5PN scattering angle.
  • standard math The scatter-to-bound map (3.11) from prior literature is valid for local Hamiltonians without hereditary terms.
    The map is used as a consistency check for the conservative 2PN scattering angle and periastron advance, not as an input to the main derivation.

how reviews work

0 comments
Cite this review

Pith. "Pith review of Quasi-Keplerian parametrization for compact binaries on hyperbolic orbits in scalar-tensor theories at second post-Newtonian order." pith.science (2026). https://pith.science/paper/4ABYNFVG

@misc{pith2026250413829,
  author       = {Pith},
  title        = {Pith review of: Quasi-Keplerian parametrization for compact binaries on hyperbolic orbits in scalar-tensor theories at second post-Newtonian order},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/4ABYNFVG}},
  note         = {Machine review of arXiv:2504.13829}
}
read the original abstract

We obtain the generalized quasi-Keplerian parametrization for compact binaries on quasihyperbolic orbits at second post-Newtonian (2PN) order in a class of massless scalar-tensor theories, extending the analogous results for quasielliptic systems arXiv:2401:06844. In particular, we compute the conservative scattering angle and impact parameter at 2PN. Our results are consistent with the 2PN conservative scatter-to-bound map in these theories between the scattering angle and the periastron advance. We then compute the total energy and angular momentum lost by the system and study the limiting cases of parabolic orbits and bremsstrahlung, including a re-expansion of our results at seventh post-Minkowskian order. Flux-balance arguments then allow us to compute the dissipative contributions to the scattering angle at 1.5PN and 2.5PN, completing the full scattering angle at 2.5PN in these theories. Finally, we obtain, in general relativity, an expression for the 3PN impact parameter in the conservative sector, correcting previous literature.

Discussion (0). Continue with ORCID to comment.

Reference graph

Works this paper leans on

83 extracted references · 24 canonical work pages

  1. [58]

    Sennett, S

    N. Sennett, S. Marsat, and A. Buonanno, Gravitational waveforms in scalar-tensor gravity at 2PN relative order, Phys. Rev. D 94, 084003 (2016), arXiv:1607.01420 [gr- qc]

    arXiv 2016

  2. [1]

    The scattering angle χ The scattering angle is defined as χ = ∆ ϕ − π, where the accumulated azimuthal angle is defined as ∆ ϕ≡ limt→+∞ϕ(t)− limt→−∞ϕ(t), as shown in [20, 73]. It reads at 2PN order (see also the Supplemental Material [62]), χ =−π + √ A C 2 3B2− 2AC D1F B2−AC − 2CI 1 ! + √ A 24C 4 (B2−AC)2 315B5D2 1F− 570AB3CD 2 1F + 243A2BC 2D2 1F − 180B5...

  3. [2]

    special rel- ativistic

    The impact parameter b The impact parameter was defined in Refs. [16, 63] as b = lim r→∞ |r× v| v∞ , (3.8) which is not a manifestly gauge invariant definition. The structure of Eqs. (3.2a) and (3.3a), together with Eq. (3.8), means that, at 2PN, the impact parameter then simply reads b = F√ A . (3.9) In fact, from the structure of the QK parametrization ...

    1942

  4. [3]

    15 8 − 1 8 ¯δ+ + 15 8 ¯γ + 15 32 ¯γ2− 1 8 ¯δ−δ +ν − 3 4 + 1 4 ¯β+− 1 2 ¯γ− 1 4 ¯β−δ # +ȷ7/2

    Then, PN corrections to these roots are obtained it- eratively by requiring that they cancel R(s), ignoring higher-order PN corrections. One can then factorize the polynomial as R(s) = (s+−s)(s−s−) ˜R(s). (A1) The QK parameters ¯ar =−(s+ +s−)/(2s+s−)> 0 and ¯er = (s+−s−)/(s+ +s−)> 1 are then trivial to obtain, where we recalls± = 1/r±. Following [16], it ...

    1942

  5. [4]

    K¨ alin and R

    G. K¨ alin and R. A. Porto, From Boundary Data to Bound States, J. High Energ. Phys. 01, 072, arXiv:1910.03008 [hep-th]

    arXiv 1910

  6. [5]

    K¨ alin and R

    G. K¨ alin and R. A. Porto, From boundary data to bound states. Part II. Scattering angle to dynamical invariants (with twist), J. High Energ. Phys. 02, 120, arXiv:1911.09130 [hep-th]

    arXiv 1911

  7. [6]

    G. Cho, G. K¨ alin, and R. A. Porto, From boundary data to bound states. Part III. Radiative effects, JHEP 04, 154, [Erratum: JHEP 07, 002 (2022)], arXiv:2112.03976 [hep-th]

    arXiv 2022

  8. [7]

    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

Show all 83 references
  1. [8]

    Cheung, I

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

    2018 arXiv

  2. [9]

    Badger, J

    S. Badger, J. Henn, J. C. Plefka, and S. Zoia, Scattering Amplitudes in Quantum Field Theory, Lect. Notes Phys. 1021, pp. (2024), arXiv:2306.05976 [hep-th]

    2024 arXiv

  3. [10]

    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, Nature 641, 603 (2025), arXiv:2411.11846 [hep-th]

    2025 arXiv

  4. [11]

    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]

    2024 arXiv

  5. [12]

    Frellesvig, R

    H. Frellesvig, R. Morales, and M. Wilhelm, Calabi- Yau Meets Gravity: A Calabi-Yau Threefold at Fifth Post-Minkowskian Order, Phys. Rev. Lett. 132, 201602 (2024), arXiv:2312.11371 [hep-th]

    2024 arXiv

  6. [13]

    Damour and N

    T. Damour and N. Deruelle, General relativistic celes- tial mechanics of binary systems I. The post-Newtonian motion, Ann. Inst. Henri Poincar´ e A 43, 107 (1985), Numdam:AIHPA 1985 43 1 107 0

    1985

  7. [14]

    Damour and G

    T. Damour and G. Sch¨ afer, Higher order relativistic pe- riastron advances in binary pulsars, Nuovo Cim. B101, 127 (1988)

    1988

  8. [15]

    Sch¨ afer and N

    G. Sch¨ afer and N. Wex, Second post-Newtonian morion of compact binaries, Phys. Lett. A 174, 196 (1993), er- ratum Phys. Lett. A 177, 461 (1993)

    1993

  9. [16]

    Memmesheimer, A

    R.-M. Memmesheimer, A. Gopakumar, and G. Schae- fer, Third post-Newtonian accurate generalized quasi- Keplerian parametrization for compact binaries in eccen- tric orbits, Phys. Rev. D 70, 104011 (2004), arXiv:gr- qc/0407049

    2004

  10. [17]

    G. Cho, S. Tanay, A. Gopakumar, and H. M. Lee, Gen- eralized quasi-Keplerian solution for eccentric, nonspin- ning compact binaries at 4PN order and the associated 24 inspiral-merger-ringdown waveform, Phys. Rev. D 105, 064010 (2022), arXiv:2110.09608 [gr-qc]

    2022 arXiv

  11. [18]

    Blanchet and G

    L. Blanchet and G. Sch¨ afer, Higher order gravitational radiation losses in binary systems, Mon. Not. Roy. As- tron. Soc. 239, 845 (1989)

    1989

  12. [19]

    G. Cho, A. Gopakumar, M. Haney, and H. M. Lee, Grav- itational waves from compact binaries in post-Newtonian accurate hyperbolic orbits, Phys. Rev. D 98, 024039 (2018), arXiv:1807.02380 [gr-qc]

    2018 arXiv

  13. [20]

    D. Bini, T. Damour, and A. Geralico, Sixth post- Newtonian nonlocal-in-time dynamics of binary systems, Phys. Rev. D 102, 084047 (2020), arXiv:2007.11239 [gr- qc]

    2020 arXiv

  14. [21]

    G. Cho, S. Dandapat, and A. Gopakumar, Third or- der post-Newtonian gravitational radiation from two- body scattering: Instantaneous energy and angular mo- mentum radiation, Phys. Rev. D 105, 084018 (2022), arXiv:2111.00818 [gr-qc]

    2022 arXiv

  15. [22]

    Cho, Third post-Newtonian gravitational radiation from two-body scattering

    G. Cho, Third post-Newtonian gravitational radiation from two-body scattering. II. Hereditary energy radia- tion, Phys. Rev. D 105, 104035 (2022), arXiv:2203.10872 [gr-qc]

    2022 arXiv

  16. [23]

    Bini and T

    D. Bini and T. Damour, Gravitational scattering of two black holes at the fourth post-Newtonian approximation, Phys. Rev. D 96, 064021 (2017), arXiv:1706.06877 [gr- qc]

    2017 arXiv

  17. [24]

    D. Bini, T. Damour, and A. Geralico, Radiative contri- butions to gravitational scattering, Phys. Rev. D 104, 084031 (2021), arXiv:2107.08896 [gr-qc]

    2021 arXiv

  18. [25]

    C. M. Will, Theory and Experiment in Gravitational Physics (Cambridge University Press, 2018)

    2018

  19. [26]

    Yunes and F

    N. Yunes and F. Pretorius, Fundamental Theoretical Bias in Gravitational Wave Astrophysics and the Parame- terized Post-Einsteinian Framework, Phys. Rev. D 80, 122003 (2009), arXiv:0909.3328 [gr-qc]

    2009 arXiv

  20. [27]

    Blanchet and B

    L. Blanchet and B. S. Sathyaprakash, Signal analysis of gravitational wave tails, Class. Quant. Grav. 11, 2807 (1994)

    1994

  21. [28]

    C. K. Mishra, K. G. Arun, B. R. Iyer, and B. S. Sathyaprakash, Parametrized tests of post-Newtonian theory using Advanced LIGO and Einstein Telescope, Phys. Rev. D 82, 064010 (2010), arXiv:1005.0304 [gr-qc]

    2010 arXiv

  22. [29]

    Jordan, Schwerkraft und Weltall (F

    P. Jordan, Schwerkraft und Weltall (F. Vieweg & Sohn, Braunschweig, 1955)

    1955

  23. [30]

    Fierz, ¨Uber die physikalische Deutung der erweiterten Gravitationstheorie P

    M. Fierz, ¨Uber die physikalische Deutung der erweiterten Gravitationstheorie P. Jordans, Helv. Phys. Acta 29, 128 (1956)

    1956

  24. [31]

    Brans and R

    C. Brans and R. Dicke, Mach’s principle and a relativistic theory of gravity, Phys. Rev. 124, 925 (1961)

    1961

  25. [32]

    Nordtvedt, Jr., Post-Newtonian metric for a general class of scalar tensor gravitational theories and observa- tional consequences, Astrophys

    K. Nordtvedt, Jr., Post-Newtonian metric for a general class of scalar tensor gravitational theories and observa- tional consequences, Astrophys. J. 161, 1059 (1970)

    1970

  26. [33]

    R. V. Wagoner, Scalar tensor theory and gravitational waves, Phys. Rev. D 1, 3209 (1970)

    1970

  27. [34]

    Shiralilou, T

    B. Shiralilou, T. Hinderer, S. M. Nissanke, N. Ortiz, and H. Witek, Post-Newtonian gravitational and scalar waves in scalar-Gauss–Bonnet gravity, Class. Quant. Grav. 39, 035002 (2022), arXiv:2105.13972 [gr-qc]

    2022 arXiv

  28. [35]

    R. F. Diedrichs, D. Schmitt, and L. Sagunski, Binary sys- tems in massive scalar-tensor theories: Next-to-leading order gravitational wave phase from effective field the- ory, Phys. Rev. D 110, 104073 (2024), arXiv:2311.04274 [gr-qc]

    2024 arXiv

  29. [36]

    Sch¨ on and D

    O. Sch¨ on and D. D. Doneva, Tensor-multiscalar gravity: Equations of motion to 2.5 post-Newtonian order, Phys. Rev. D 105, 064034 (2022), arXiv:2112.07388 [gr-qc]

    2022 arXiv

  30. [37]

    Taherasghari and C

    F. Taherasghari and C. M. Will, Compact binary systems in Einstein-Æther gravity: Direct integration of the re- laxed field equations to 2.5 post-Newtonian order, Phys. Rev. D 108, 124026 (2023), arXiv:2308.13243 [gr-qc]

    2023 arXiv

  31. [38]

    Higashino and S

    Y. Higashino and S. Tsujikawa, Inspiral gravitational waveforms from compact binary systems in Horn- deski gravity, Phys. Rev. D 107, 044003 (2023), arXiv:2209.13749 [gr-qc]

    2023 arXiv

  32. [39]

    Wu and Y

    W.-H. Wu and Y. Tang, Post-Newtonian binary dynam- ics in the effective field theory of Horndeski gravity, Chin. Phys. C 48, 035101 (2024), arXiv:2312.02507 [gr-qc]

    2024 arXiv

  33. [40]

    Chowdhuri, R

    A. Chowdhuri, R. K. Singh, K. Kangsabanik, and A. Bhattacharyya, Gravitational radiation from hyper- bolic encounters in the presence of dark matter, Phys. Rev. D 109, 124056 (2024), arXiv:2306.11787 [gr-qc]

    2024 arXiv

  34. [41]

    Damour and G

    T. Damour and G. Esposito-Far` ese, Tensor multiscalar theories of gravitation, Class. Quant. Grav. 9, 2093 (1992)

    1992

  35. [42]

    Damour and G

    T. Damour and G. Esposito-Far` ese, Nonperturbative strong field effects in tensor-scalar theories of gravitation, Phys. Rev. Lett. 70, 2220 (1993)

    1993

  36. [43]

    Damour and G

    T. Damour and G. Esposito-Far` ese, Testing for Preferred-Frame Effects in Gravity with Artificial Earth Satellites, Phys. Rev. D 49, 1693 (1994), arXiv:9311034 [gr-qc]

    1994

  37. [44]

    Damour and G

    T. Damour and G. Esposito-Far` ese, Testing gravity to second post-Newtonian order: A Field theory approach, Phys. Rev. D 53, 5541 (1996), arXiv:gr-qc/9506063

    1996 arXiv

  38. [45]

    Damour and G

    T. Damour and G. Esposito-Far` ese, Gravitational-wave versus binary-pulsar tests of strong-field gravity, Phys. Rev. D 58, 042001 (1998), arXiv:9803031 [gr-qc]

    1998

  39. [46]

    A. G. Wiseman, Coalescing binary systems of compact objects to (post)5/2 Newtonian order. 2. Higher order wave forms and radiation recoil, Phys. Rev. D 46, 1517 (1992)

    1992

  40. [47]

    Will and A

    C. Will and A. Wiseman, Gravitational radiation from compact binary systems: Gravitational waveforms and energy loss to second post-Newtonian order, Phys. Rev. D 54, 4813 (1996), arXiv:gr-qc/9608012 [gr-qc]

    1996 arXiv

  41. [49]

    R. N. Lang, Compact binary systems in scalar-tensor gravity. II. Tensor gravitational waves to second post- Newtonian order, Phys. Rev. D 89, 084014 (2014), arXiv:1310.3320 [gr-qc]

    2014 arXiv

  42. [50]

    R. N. Lang, Compact binary systems in scalar-tensor gravity. III. Scalar waves and energy flux, Phys. Rev. D 91, 084027 (2015), arXiv:1411.3073 [gr-qc]

    2015 arXiv

  43. [51]

    Bernard, Dynamics of compact binary systems in scalar-tensor theories: Equations of motion to the third post-Newtonian order, Phys

    L. Bernard, Dynamics of compact binary systems in scalar-tensor theories: Equations of motion to the third post-Newtonian order, Phys. Rev. D 98, 044004 (2018), arXiv:1802.10201 [gr-qc]

    2018 arXiv

  44. [52]

    Bernard, Dynamics of compact binary systems in scalar-tensor theories: II

    L. Bernard, Dynamics of compact binary systems in scalar-tensor theories: II. Center-of-mass and conserved quantities to 3PN order, Phys. Rev. D99, 044047 (2019), arXiv:1812.04169 [gr-qc]

    2019 arXiv

  45. [53]

    Bernard, L

    L. Bernard, L. Blanchet, and D. Trestini, Gravitational waves in scalar-tensor theory to one-and-a-half post- Newtonian order, J. Cosmol. Astropart. Phys. 08 (08), 25 008, arXiv:2201.10924 [gr-qc]

    arXiv

  46. [54]

    Bernard, Dipolar tidal effects in scalar-tensor theories, Phys

    L. Bernard, Dipolar tidal effects in scalar-tensor theories, Phys. Rev. D 101, 021501 (2020), arXiv:1906.10735 [gr- qc]

    2020 arXiv

  47. [55]

    Bernard, E

    L. Bernard, E. Dones, and S. Mougiakakos, Tidal effects up to next-to-next-to-leading post-Newtonian order in massless scalar-tensor theories, Phys. Rev. D109, 044006 (2024), arXiv:2310.19679 [gr-qc]

    2024 arXiv

  48. [56]

    Blanchet, Luc and Faye, Guillaume and Henry, Quentin and Larrouturou, Fran¸ cois and Trestini, David, Gravitational-Wave Phasing of Quasicircular Com- pact Binary Systems to the Fourth-and-a-Half Post- Newtonian Order, Phys. Rev. Lett. 131, 121402 (2023), arXiv:2304.11185 [gr-qc]

    2023 arXiv

  49. [57]

    Damour and G

    T. Damour and G. Esposito-Far` ese, Tensor - scalar grav- ity and binary pulsar experiments, Phys. Rev. D54, 1474 (1996), arXiv:9602056 [gr-qc]

    1996

  50. [59]

    Trestini, Quasi-Keplerian parametrization for eccen- tric compact binaries in scalar-tensor theories at second post-Newtonian order and applications, Phys

    D. Trestini, Quasi-Keplerian parametrization for eccen- tric compact binaries in scalar-tensor theories at second post-Newtonian order and applications, Phys. Rev. D 109, 104003 (2024), arXiv:2401.06844 [gr-qc]

    2024 arXiv

  51. [60]

    Trestini, Gravitational waves from quasielliptic com- pact binaries in scalar-tensor theory to one-and-a-half post-Newtonian order, (2024), arXiv:2410.12898 [gr-qc]

    D. Trestini, Gravitational waves from quasielliptic com- pact binaries in scalar-tensor theory to one-and-a-half post-Newtonian order, (2024), arXiv:2410.12898 [gr-qc]

    2024 arXiv

  52. [61]

    Jain, Gravitational scattering up to third post- Newtonian approximation for conservative dynamics: Scalar-tensor theories, Phys

    T. Jain, Gravitational scattering up to third post- Newtonian approximation for conservative dynamics: Scalar-tensor theories, Phys. Rev. D 108, 104071 (2023), arXiv:2304.09052 [gr-qc]

    2023 arXiv

  53. [62]

    D. Bini, A. Geralico, C. Kavanagh, A. Pound, and D. Usseglio, Post-Minkowskian self-force in the low- velocity limit: Scalar field scattering, Phys. Rev. D 110, 064050 (2024), arXiv:2406.15878 [gr-qc]

    2024 arXiv

  54. [63]

    Bhattacharyya, D

    A. Bhattacharyya, D. Ghosh, S. Ghosh, and S. Pal, Ob- servables from classical black hole scattering in Scalar- Tensor theory of gravity from worldline quantum field theory, JHEP 04, 015, arXiv:2401.05492 [hep-th]

    arXiv

  55. [64]

    Bhattacharyya, D

    A. Bhattacharyya, D. Ghosh, S. Ghosh, and S. Pal, Boot- strapping the spinning two body problem in dynamical Chern-Simons gravity using worldline QFT, JHEP 04, 175, arXiv:2407.07195 [hep-th]

    arXiv

  56. [65]

    See the ancillary file Supplemental Material.dat.wl for various results of this paper in machine-readable form (Wolfram Language)

  57. [66]

    De Vittori, A

    L. De Vittori, A. Gopakumar, A. Gupta, and P. Jet- zer, Gravitational waves from spinning compact binaries in hyperbolic orbits, Phys. Rev. D 90, 124066 (2014), arXiv:1410.6311 [gr-qc]

    2014 arXiv

  58. [67]

    C. M. Will and K. Nordtvedt Jr, Conservation laws and preferred frames in relativistic gravity. I. Preferred-frame theories and an extended PPN formalism, The Astro- physical Journal 177, 757 (1972)

    1972

  59. [68]

    Mirshekari and C

    S. Mirshekari and C. M. Will, Compact binary systems in scalar-tensor gravity: Equations of motion to 2.5 post-Newtonian order, Phys. Rev. D 87, 084070 (2013), arXiv:1301.4680 [gr-qc]

    2013 arXiv

  60. [69]

    D. M. Eardley, Observable effects of a scalar gravitational field in a binary pulsar, Astrophys. J. Lett. 196, L59 (1975)

    1975

  61. [70]

    Nordtvedt, ˙G/G and a cosmological acceleration of gravitationally compact bodies, Phys

    K. Nordtvedt, ˙G/G and a cosmological acceleration of gravitationally compact bodies, Phys. Rev. Lett. 65, 953 (1990)

    1990

  62. [71]

    Blanchet and G

    L. Blanchet and G. Faye, Hadamard regularization, J. Math. Phys. 41, 7675 (2000), arXiv:gr-qc/0004008 [gr- qc]

    2000 arXiv

  63. [72]

    Blanchet, T

    L. Blanchet, T. Damour, and G. Esposito-Far` ese, Dimen- sional regularization of the third post-Newtonian dynam- ics of point particles in harmonic coordinates, Phys. Rev. D 69, 124007 (2004), arXiv:gr-qc/0311052 [gr-qc]

    2004 arXiv

  64. [73]

    Blanchet, T

    L. Blanchet, T. Damour, G. Esposito-Far` ese, and B. R. Iyer, Dimensional regularization of the third post- Newtonian gravitational wave generation of two point masses, Phys. Rev. D 71, 124004 (2005), arXiv:gr- qc/0503044

    2005

  65. [74]

    Blanchet and T

    L. Blanchet and T. Damour, Radiative gravitational fields in general relativity. I. general structure of the field outside the source, Phil. Trans. Roy. Soc. Lond. A 320, 379 (1986)

    1986

  66. [75]

    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]

    2014 arXiv

  67. [76]

    Bini and T

    D. Bini and T. Damour, Gravitational radiation reaction along general orbits in the effective one-body formalism, Phys. Rev. D 86, 124012 (2012), arXiv:1210.2834 [gr-qc]

    2012 arXiv

  68. [77]

    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. D 94, 104015 (2016), arXiv:1609.00354 [gr-qc]

    2016 arXiv

  69. [78]

    Bini and T

    D. Bini and T. Damour, Gravitational spin-orbit cou- pling in binary systems at the second post-Minkowskian approximation, Phys. Rev. D 98, 044036 (2018), arXiv:1805.10809 [gr-qc]

    2018 arXiv

  70. [79]

    Blanchet and T

    L. Blanchet and T. Damour, Hereditary effects in gravi- tational radiation, Phys. Rev. D 46, 4304 (1992)

    1992

  71. [80]

    D. Bini, T. Damour, and A. Geralico, Radiated momen- tum and radiation reaction in gravitational two-body scattering including time-asymmetric effects, Phys. Rev. D 107, 024012 (2023), arXiv:2210.07165 [gr-qc]

    2023 arXiv

  72. [81]

    Junker and G

    W. Junker and G. Sch¨ afer, Binary systems: higher order gravitational radiation damping and wave emission, Mon. Not. Roy. Astron. Soc. 254, 146 (1992)

    1992

  73. [82]

    Iyer and C

    B. Iyer and C. Will, Post-Newtonian gravitational radia- tion reaction for two-body systems: Nonspinning bodies, Phys. Rev. D 52, 6882 (1995)

    1995

  74. [83]

    Blanchet, G

    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, 065015 (2025), arXiv:2407.18295 [gr-qc]

    2025 arXiv

  75. [84]

    Barack et al

    L. Barack et al. , Comparison of post-Minkowskian and self-force expansions: Scattering in a scalar charge toy model, Phys. Rev. D 108, 024025 (2023), arXiv:2304.09200 [hep-th]

    2023 arXiv

Pith tools

Reviewed August 16, 2026 · model on record in the stance chip above.