arXiv subjects

Thibault Damour

Publications and source records attributed to Thibault Damour.

At least 19 recordsLinked to original sources

arXiv2026

Octupolar bremsstrahlung waveform up to the two-loop level and the third-and-a-half post-Newtonian accuracy

Extending our recent work (which focussed on the even-parity quadrupolar part of the waveform), we compute the even-parity octupolar contribution, $U_3$, to the gravitational waveform $W \equiv \frac{c^4 r}{4G} \bar m^{i} \bar m^{j } h_{i j}$ emitted during the scattering of two masses. We work within the Multipolar Post-Minkowskian (MPM) formalism, and use the 3.5 Post-Newtonian (PN) accurate radiation-reacted quasi-Keplerian representation of the hyperbolic motion. We explicitly evaluate the frequency-domain value $\hat U_3(\omega, \theta,\phi)$ of $U_3$ up to the 2-loop level, i.e. $ O(G^4)$ contributions to $h_{ij}(\omega, \theta,\phi)$, corresponding to $O(G^3)$ contributions to $\hat U_3(\omega, \theta,\phi)$. As a crucial partial confirmation of our result, we find that the 1-loop truncation of our 3.5 PN frequency-domain MPM waveform agrees with corresponding existing Effective Field Theory (EFT) results when taking into account exactly the {\it same} (2.5PN-level) difference in the definitions of the center-of-mass origins within the two formalisms that was deduced from our previous quadrupolar comparison.

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arXiv2026

Radiated Energy Spectrum, Radiated Angular Distribution and Non-linear Memory from the One-loop Gravitational Bremsstrahlung Waveform

The frequency-domain gravitational waveform emitted by the scattering of two non-spinning massive particles has recently been derived at next-to-leading, \textit{i.e.} one-loop, post-Minkowskian order, $h(\omega, \theta,\phi) \sim G^2 + G^3$. Building on this one-loop-accurate frequency-domain gravitational waveform, we successively derive the spectral gravitational-wave (GW) radiance, $dE^{\rm gw}/(d\omega d\Omega)$, the radiated GW energy spectrum, $dE^{\rm gw}/d\omega$, and the radiated GW angular distribution, $dE^{\rm gw}/d\Omega$, up to order $G^4$ included. We deduce from the radiated angular distribution the multipole expansion of the non-linear memory up to order $G^5$ included, thereby extending previous results. We work in the center-of-mass frame, and our results reach the fractional 7.5PN accuracy. For completeness, we include the tree-level information (considered in the center-of-mass frame).

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arXiv2026

Quadrupolar bremsstrahlung waveform at the third-and-a-half post-Newtonian accuracy

We study the quadrupolar part of the gravitational waveform $h_{ij}$ (encoded in the helicity-($-2)$ radiative quadrupole moment $U_2 = \frac{1}{2!} \bar m^{i} \bar m^{j } U_{i j} \in\frac{R}{4G} \bar m^{i} \bar m^{j } h_{i j}\equiv W $) emitted during the scattering of two masses. Working within the Multipolar Post-Minkowskian (MPM) formalism, we compute the time-domain value of $U_2$ at the third-and-a-half post-Newtonian (3.5PN) accuracy by using the 3.5PN radiation-reacted quasi-Keplerian representation of the hyperbolic motion. We then explicitly evaluate the {\it frequency-domain} value of $U_2$ up to the 2-loop level, i.e. $ O(G^4)$ contributions to $h_{ij}(ω, θ,ϕ)$, corresponding to $O(G^3)$ contributions to $\hat U_2(ω, θ,ϕ)$. The nonlinear memory contribution to the waveform in the center-of-mass frame is computed too, and checked against the soft-limit of the waveform. The 1-loop truncation of our 3.5PN frequency-domain MPM waveform is found to agree with corresponding existing Effective Field Theory (EFT) results when subtracting the dipolar part of the Veneziano-Vilkovisky supertranslation connecting the MPM and EFT Bondi-Metzner-Sachs (BMS) frames.

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arXiv2026

High-order effective-one-body tidal interactions and gravitational scattering

Using state-of-the-art scattering results in post-Minkowskian (PM) gravity, we improve the tidal sector of four different flavors of the effective-one-body (EOB) formalism. We notably explore both adiabatic and post-adiabatic gravitoelectric and gravitomagnetic quadrupolar tidal effects at the next-to-next-to-leading PM-order. When comparing the predictions of the so-constructed Lagrange-PM-tidal version of EOB to recent numerical-relativity data on the scattering of neutron stars, we find improved agreement with respect to existing EOB models and PM expansions. Our work lays the foundation for the development of an accurate tidal sector of the PM EOB models, and points out the need to explore improved resummation schemes in PN EOB for bound and circularized orbits.

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arXiv2026

A novel Lagrange-multiplier approach to the effective-one-body dynamics of binary systems in post-Minkowskian gravity

We present a new approach to the conservative dynamics of binary systems, within the effective one-body (EOB) framework, based on the use of a Lagrange multiplier to impose the mass-shell constraint. When applied to the post-Minkowskian (PM) description of the two-body problem in Einsteinian gravity, this Lagrange-EOB (LEOB) approach allows for a new formulation of the conservative dynamics that avoids the drawbacks of the recursive definition of EOB-PM Hamiltonians. Using state-of-the-art expressions of the resummed waveform and radiation reaction, we apply our new formalism to the construction of an aligned-spin, quasi-circular, inspiraling EOB waveform model, called {\tt LEOB-PM}, that incorporates analytical information up to the 4PM level, completed by 4PN contributions up to the sixth order in eccentricity, in the orbital sector, and by 4.5PN contributions, in the spin-orbit sector. In the nonspinning case, we find that an uncalibrated LEOB-PM model delivers maximum EOB/NR unfaithfulness ${\bar{F}}_{\rm EOBNR}$ (with the Advanced LIGO noise in the total mass range $10-200M_\odot$) varying between $0.2\%$ and $1\%$ over all the nonspinning dataset of the Simulating eXtreme Spacetime (SXS) Numerical Relativity (NR) catalog up to mass ratio $q=15$. It also delivers excellent phasing agreement with the $q=32$ configuration of the RIT catalog. We also found consistency between binding energies within a few percent at the NR merger location. Then, when NR-informing the dynamics of the model (both orbital and spinning sectors) by using 17 SXS dataset, we find that the EOB/NR unfaithfulness (compared to 530 spin-aligned SXS waveforms) has a median value of $5.39\times 10^{-4}$, or $6.13\times 10^{-4}$ (depending on the spin-spin interactions), reaching at most $\sim 1\%$ in some of the high-spin corners.

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arXiv2025

Gravitational scattering of solitonic boson stars: Analytics vs Numerics

We study the scattering of boson-star binaries, taking into account three effects: point-mass gravitational, tidal, and short-range scalar-field interactions. We compare analytic results to the scattering angle extracted from four sequences of numerical-relativity simulations at fixed energy and varying impact parameter. The very good agreement exhibits the attractive (repulsive) effect of in-phase (out-of-phase) binaries, wich dominates at small impact parameters. We thus obtain the first effective-one-body potential, central for the construction of analytic gravitational-wave templates.

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arXiv2025

An Unfinished Collaboration with A. A. Starobinsky

The present text summarizes some of the results obtained in 2008 during the initial stages of a collaboration with Starobinsky which remained unfinished. The collaboration was an attempt to apply the stochastic approach to infrared (IR) quantum-gravity effects in an inflationary spacetime.

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arXiv2025

Remembering Yvonne Choquet-Bruhat

I describe the impact of some of the mathematical results of Yvonne Choquet-Bruhat on gravitational physics, as well as the evolution of my interactions with her over the years.

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arXiv2025

High-post-Newtonian-order dynamical effects induced by tail-of-tail interactions in a two body system

Starting from the recently derived conservative tail-of-tail action [D. Bini and T. Damour, arXiv:2504.20204 [hep-th]] we compute several dynamical observables of binary systems (Delaunay Hamiltonian, scattering angle), at the 6.5 post-Newtonian accuracy and up to the 8th post-Minkowskian order. We find perfect agreement with previous self-force results, and (when inserting a recent high-post-Newtonian order derivation of radiated angular momentum [A. Geralico, arXiv:2507.03442 [gr-qc]]) with state-of-the-art post-Minkowskian scattering results [M.~Driesse et al., Nature \textbf{641}, no.8063, 603-607 (2025)].

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arXiv2025

High Precision Black Hole Scattering: Tutti Frutti vs Worldline Effective Field Theory

We consider black hole scattering up to the fifth Post Minkowskian ($G^5$) order and compare the predictions of the Tutti Frutti formalism to the results obtained within two different versions of Worldline Effective Field Theory. At the $G^4$ order we highlight the complete agreement between Tutti Frutti results and the results of [C. Dlapa et al., Phys. Rev. Lett. \textbf{130}, no.10, 101401 (2023)], and show how the Tutti Frutti approach allows one to extract the $O(G^3)$ angular momentum loss from the $O(G^4)$ impulse. We compare the sixth Post-Newtonian (6PN) accurate Tutti Frutti predictions to the recent results of [M. Driesse et al., arXiv:2411.11846 [hep-th]], which are at the $G^5$ order, and at the leading order in the two mass ratios, finding complete agreement. We highlight that this agreement involves the presence at the 5.5PN level of a nonlocal tail-of-tail contribution to the scattering (first computed in [D. Bini et al., Phys. Rev. D \textbf{102}, no.8, 084047 (2020)]), and involves, at the 6PN level, the presence of a $O(G^4)$ contribution to the angular momentum loss [C. Heissenberg, arXiv:2501.02904 [hep-th]]. At the second order in the mass ratios of the $O(G^5)$ order we predict two independent gauge-invariant observables to high-PN accuracy.

hep-th↗

arXiv2025

A Non-linear Massive Gravity Theory of Geometric Origin

We study the number of propagating degrees of freedom, at non-linear order, in torsion gravity theories, a class of modified theories of gravity that include a propagating torsion in addition to the metric. We focus on a three-parameter subfamily of theories (``torsion bigravity") that contains, at linear order, only two physical excitations: a massless spin-2 one (with two degrees of freedom) and a massive spin-2 one (with five degrees of freedom). We study the dynamics of the massive spin-2 field in the limit where the torsion field decouples from the metric. The number of degrees of freedom of the torsion field is found to {\it change, at non-linear order, from five to nine}.

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arXiv2024

Conservative binary dynamics beyond order $α^5$ in electrodynamics

We compute the conservative scattering angle of two classical charged particles at the sixth order in electromagnetic coupling, and at the fourth order in velocity, thereby going beyond the current state of the art [fifth order in coupling, derived by Bern {\it et al.}, Phys. Rev. Lett. \textbf{132}, 251601 (2024)]. Our result is obtained by using the electromagnetic version of the Effective One-Body formalism to transfer information from the exact circular binary-charge solution of Schild [Phys. Rev. \textbf{131}, 2762 (1963)] to the post-Lorentzian expansion of the scattering angle.

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arXiv2024

Explicit solution of the gravitational two-body problem at the second post-Minkowskian order

The worldlines (in harmonic coordinates) of two gravitationally interacting massive bodies at the second post-Minkowskian order are described in explicit form. Both the conservative case and the radiation-reacted case are considered. We use our results to check the changes, during scattering, of the individual momenta, as well as of the total angular momentum. High post-Newtonian order values of the $O(G^2)$ radiation-reaction acceleration components are provided for checks of future post-Newtonian computations.

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arXiv2024

Gravitational Bremsstrahlung Waveform at the fourth Post-Minkowskian order and the second Post-Newtonian level

Using the Multipolar Post-Minkowskian formalism, we compute the frequency-domain waveform generated by the gravitational scattering of two nonspinning bodies at the fourth post-Minkowskian order ($O(G^4)$, or two-loop order), and at the fractional second Post-Newtonian accuracy ($O(v^4/c^4)$). The waveform is decomposed in spin-weighted spherical harmonics and the needed radiative multipoles, $U_{\ell m}(ω), V_{\ell m}(ω)$, are explicitly expressed in terms of a small number of master integrals. The basis of master integrals contains both (modified) Bessel functions, and solutions of inhomogeneous Bessel equations with Bessel-function sources. We show how to express the latter in terms of Meijer G functions. The low-frequency expansion of our results is checked againg existing classical soft theorems. We also complete our previous results on the $O(G^2)$ bremsstrahlung waveform by computing the $O(G^3)$ spectral densities of radiated energy and momentum, in the rest frame of one body, at the thirtieth order in velocity.

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arXiv2024

Gravitational Waveform: A Tale of Two Formalisms

We revisit the quantum-amplitude-based derivation of the gravitational waveform emitted by the scattering of two spinless massive bodies at the third order in Newton's constant, $h \sim G+G^2+G^3$ (one-loop level), and correspondingly update its comparison with its classically-derived multipolar-post-Minkowskian counterpart. A spurious-pole-free reorganization of the one-loop five-point amplitude substantially simplifies the post-Newtonian expansion. We find complete agreement between the two results up to the fifth order in the small velocity expansion after taking into account three subtle aspects of the amplitude derivation: (1) in agreement with [arXiv:2312.07452 [hep-th]], the term quadratic in the amplitude in the observable-based formalism [JHEP 02, 137 (2019)] generates a frame rotation by half the classical scattering angle; (2) the dimensional regularization of the infrared divergences of the amplitude introduces an additional $(d-4)/(d-4)$ finite term; and (3) zero-frequency gravitons are found to contribute additional terms both at order $h \sim G^1$ and at order $h \sim G^3$ when including disconnected diagrams in the observable-based formalism.

hep-th↗

arXiv2024

Fourth Post-Minkowskian Local-in-Time Conservative Dynamics of Binary Systems

We compute the purely local-in-time (scale-free and logarithm-free) part of the conservative dynamics of gravitationally interacting two-body systems at the fourth post-Minkowskian order, and at the thirtiest order in velocity. The gauge-invariant content of this fourth post-Minkowskian local dynamics is given in two ways: (i) its contribution to the on-shell action (for both hyperboliclike and ellipticlike motions); and (ii) its contribution to the Effective One Body Hamiltonian (in energy gauge). Our computation capitalizes on the Tutti Frutti approach [Phys. Rev. Lett. \textbf{123}, no.23, 231104 (2019)], and on recent post-Minkowskian advances [Phys. Rev. Lett. \textbf{128}, no.16, 161103 (2022)], [Phys. Rev. Lett. \textbf{128}, no.16, 161104 (2022)], and [Phys. Rev. Lett. \textbf{132}, no.22, 221401 (2024)].

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arXiv2024

Comparing One-loop Gravitational Bremsstrahlung Amplitudes to the Multipolar-Post-Minkowskian Waveform

We compare recent one-loop-level, scattering-amplitude-based, computations of the classical part of the gravitational bremsstrahlung waveform to the frequency-domain version of the corresponding Multipolar-Post-Minkowskian waveform result. When referring the one-loop result to the classical averaged momenta $\bar p_a = \frac12 (p_a+p'_a)$, the two waveforms are found to agree at the Newtonian and first post-Newtonian levels, as well as at the first-and-a-half post-Newtonian level, i.e. for the leading-order quadrupolar tail. However, we find that there are significant differences at the second-and-a-half post-Newtonian level, $O\left( \frac{G^2}{c^5} \right)$, i.e. when reaching: (i) the first post-Newtonian correction to the linear quadrupole tail; (ii) Newtonian-level linear tails of higher multipolarity (odd octupole and even hexadecapole); (iii) radiation-reaction effects on the worldlines; and (iv) various contributions of cubically nonlinear origin (notably linked to the quadrupole$\times$ quadrupole$\times$ quadrupole coupling in the wavezone). These differences are reflected at the sub-sub-sub-leading level in the soft expansion, $ \sim ω\ln ω$, i.e. $O\left(\frac{1}{t^2} \right)$ in the time domain. Finally, we computed the first four terms of the low-frequency expansion of the Multipolar-Post-Minkowskian waveform and checked that they agree with the corresponding existing classical soft graviton results.

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arXiv2024

Editorial note to Jean-Marie Souriau's " On the motion of spinning particles in general relativity"

The gravitational interaction of (classical and quantum) spinning bodies is currently the focus of many works using a variety of approaches. This note is a comment on a short paper by Jean-Marie Souriau, now reprinted in the GRG Golden Oldies collection. Souriau's short 1970 note was a pioneering contribution to a symplectic description of the dynamics of spinning particles in general relativity which remained somewhat unnoticed. We explain the specificity of Souriau's approach and emphasize its potential interest within the current flurry of activity on the gravitational interaction of spinning particles.

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