arXiv subjects

David Trestini

Publications and source records attributed to David Trestini.

18 recordsLinked to original sources

arXiv2026

Constants of motion and fundamental frequencies for elliptic orbits at fourth post-Newtonian order: aligned-spin contributions

For eccentric systems with aligned spins, we compute all spin contributions to the gauge-invariant conservative map between the constants of motion (energy and angular momentum) and the fundamental (radial and azimuthal) frequencies at the fourth post-Newtonian order. This extends the nonspinning map derived in [arXiv:2511.10735] to include terms that are linear, quadratic, cubic, and quartic in spin, as well as the associated spin-deformability parameters. We also obtain derived quantities such as the redshift and gyroscopic invariants, as well as circular links. We notice that the Blanchet-Iyer-Favata post-Newtonian stability criterion that determines the dimensionless frequency of the innermost stable circular orbit (ISCO) is in fact intricately related to the periastron advance for circular orbits. Finally, in the case of unbound orbits, we complete the 4PN scattering angle with all spin contributions.

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arXiv2026

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

We derive the gravitational radiation-reaction (RR) force in the harmonic coordinate system at the fourth-and-a-half post-Newtonian (4.5PN) order in the case of compact binary systems. Dimensional regularization is used to treat the ultra-violet divergences which appear at that order. We prove that the RR acceleration implies the known radiation fluxes at infinity associated with energy, angular momentum, linear momentum, and center-of-mass position. As a consistency check, we verify the manifest Lorentz invariance of the RR acceleration in harmonic coordinates. Our result should be useful for comparisons with other approaches such as the gravitational self force (GSF) and the post-Minkowskian (PM) effective field theory.

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arXiv2026

Constants of motion in gravitational self-force theory

Synergies between self-force theory and other approaches to the gravitational two-body problem have traditionally relied on calculations of gauge-invariant observables as functions of orbital frequencies. However, in self-force theory, one can also define a complete set of constants of motion: energy, azimuthal angular momentum, and radial and polar actions. Here, we outline how directly utilizing these constants allows for more straightforward comparisons and hybridizations across the parameter space, as well as more streamlined waveform generation through flux-balance laws. Restricting to the case of nonspinning binaries and first order in self-force, we compute the constants of motion and the corrections to fundamental frequencies numerically as well as analytically (to 9PN in a post-Newtonian expansion), establishing consistency with the highest-order (4PN) results available from post-Newtonian theory. We also apply the results to identify the perturbed locations of special curves in the parameter space: circular orbits and the separatrix between bound and plunging orbits.

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arXiv2025

Constants of motion and fundamental frequencies for elliptic orbits at fourth post-Newtonian order

In the case of nonspinning compact binary systems on quasi-elliptic orbits, I obtain the conservative map between the constants of motion (energy and angular momentum) and the fundamental (radial and azimuthal) frequencies at the fourth post-Newtonian order, including both instantaneous and tail contributions. This map is expressed in terms of an enhancement function of the eccentricity, which is appropriately resummed to ensure accuracy for any eccentricity; in particular, I recover known results for circular orbits. In order to obtain this map, the local dynamics are expressed using an action-angle formulation. The tail term is treated as a perturbation, which is first localized in time, then Delaunay-averaged. Both operations require a contact transformation of the phase-space variables, which I explicitly control. Using the first law of binary black hole mechanics, I then obtain the orbit-averaged redshift invariant for eccentric orbits at fourth post-Newtonian order; when properly accounting for the tail contributions, it perfectly agrees with analytical self-force at postgeodesic order [arXiv:2203.13832]. Finally, I use these results to re-express the fluxes of energy and angular momentum obtained at third post-Newtonian order in [arXiv:0711.0302] and [arXiv:0908.3854] in terms of fundamental frequencies.

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arXiv2025

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

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.

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arXiv2025

Schott term in the binding energy for compact binaries on circular orbits at fourth post-Newtonian order

The phasing for compact binary systems on circular orbits was obtained in arXiv:2304.11185 at fourth-and-a-half post-Newtonian (4.5PN) order thanks to two main ingredients: the 4PN conservative energy (associated to a nonradiative spacetime) in terms of the orbital frequency and the 4.5PN flux in terms of the waveform frequency (i.e., the half-frequency of the $(\ell,m)=(2,2)$ mode). When obtaining the phasing, a key physical postulate was made: the expression of the binding energy in terms of the waveform frequency was assumed to be identical to the expression of the conservative energy in terms of the orbital frequency. This postulate was necessary to ensure that the frequency evolution obtained through the flux-balance law (which involves the binding energy) was independent of the choice of spacetime foliation. In this work, I show that the binding energy entering the flux-balance law differs from the 4PN conservative energy by a 4PN pseudo-Schott term, associated with radiation-reaction effects due to gravitational tails. Unlike the usual Schott terms (at 2.5PN, 3.5PN and 4.5PN), the pseudo-Schott term is not a total derivative and is in fact hereditary, so it does not vanish for circular orbits. Remarkably, the binding energy thus obtained is in perfect agreement with the one obtained using the aforementioned physical postulate, which confirms that the 4.5PN phasing associated to the waveform frequency computed in arXiv:2304.11185 is indeed correct. This result is extended to the other Poincar\'e invariants, and `thermodynamic' relations between the binding energy and angular momentum are established. Finally, the chirp and phasing associated to the orbital frequency are presented at 4.5PN, including horizon-absorption effects.

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arXiv2024

Gravitational memory: new results from post-Newtonian and self-force theory

We compute the (displacement) gravitational wave memory due to a quasicircular inspiral of two black holes using a variety of perturbative techniques. Within post-Newtonian theory, we extend previous results for non-spinning binaries to 3.5PN order. Using the gravitational self-force approach, we compute the memory at first order in the mass ratio for inspirals into a Kerr black hole. We do this both numerically and via a double post-Newtonian--self-force expansion which we carry out to 5PN order. At second order in the self-force approach, near-zone calculations encounter an infrared divergence associated with memory, which is resolved through matching the near-zone solution to a post-Minkowskian expansion in the far zone. We describe that matching procedure for the first time and show how it introduces nonlocal-in-time memory effects into the two-body dynamics at second order in the mass ratio, as was also predicted by recent 5PN calculations within the effective field theory approach. We then compute the gravitational-wave memory through second order in the mass ratio (excluding certain possible memory distortion effects) and find that it agrees well with recent results from numerical relativity simulations for near-comparable-mass binaries.

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arXiv2024

Gravitational waves from quasielliptic compact binaries in scalar-tensor theory to one-and-a-half post-Newtonian order

The orbit-averaged fluxes of energy and angular momentum generated by a compact binary system of nonspinning particles are obtained in a popular class of massless scalar-tensor theories with first-and-a-half post-Newtonian (1.5PN) accuracy, i.e., 2.5PN accuracy beyond the leading -1PN dipolar radiation. The secular evolution of the orbital elements (frequency and eccentricity) are then also obtained with 1.5PN accuracy. Three technical advances were necessary to obtain these results: (i) the decomposition of the scalar dipole moment as a Fourier series at 1PN order, along with the other moments at Newtonian order, (ii) the derivation of the formula for the passage to the center-of-mass frame at 2.5PN, including a novel hereditary term arising from the contribution of the radiation, and (iii) the complete treatment of the memory-like term appearing in the angular momentum flux. Moreover, as a byproduct of this work, I revisit in the Appendix the treatment in general relativity of the memory integral appearing at 2.5PN order in the angular momentum flux [arXiv:0908.3854], and find that the spurious divergence in the initial eccentricity $e_1$ found there is cured by a careful split between AC and DC terms.

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arXiv2024

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

We compute the gravitational radiation-reaction force on a compact binary source at the fourth-and-a-half post-Newtonian (4.5PN) order of general relativity, i.e., 2PN order beyond the leading 2.5PN radiation reaction. The calculation is valid for general orbits in a general frame, but in a particular coordinate system which is an extension of the Burke-Thorne coordinate system at the lowest order. With the radiation-reaction acceleration, we derive (from first principles) the flux-balance laws associated with the energy, the angular and linear momenta, and the center-of-mass position, in a general frame and up to 4.5PN order. Restricting our attention to the frame of the center of mass, we point out that the equations of motion acquire a non-local-in-time contribution at the 4.5PN order, made of the integrated flux of linear momentum (responsible for the recoil of the source) together with the instantaneous flux of center-of-mass position. The non-local contribution was overlooked in the past literature, which assumed locality of the radiation-reaction force in the center of mass frame at 4.5PN order. We discuss the consequences of this non-local effect and obtain consistent non-local equations of motion and flux balance laws at 4.5PN order in the center-of-mass frame.

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arXiv2024

Comparison of 4.5PN and 2SF gravitational energy fluxes from quasicircular compact binaries

Recent years have seen significant advances in models of gravitational waveforms emitted by quasicircular compact binaries in two regimes: the weak-field, post-Newtonian regime, in which the gravitational wave energy flux has now been calculated to fourth-and-a-half post-Newtonian order (4.5PN) [Phys. Rev. Lett. 131}, 121402 (2023)]; and the small-mass-ratio, gravitational self-force regime, in which the flux has now been calculated to second perturbative order in the mass ratio (2SF) [Phys. Rev. Lett. 127, 151102 (2021)]. We compare these results and find agreement, showing consistency between the two (very distinct though both first-principle) perturbative calculations.

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arXiv2024

Quasi-Keplerian parametrization for eccentric compact binaries in scalar-tensor theories at second post-Newtonian order and applications

The generalized post-Keplerian parametrization for compact binaries on eccentric bound orbits is established at second post-Newtonian (2PN) order in a class of massless scalar-tensor theories. This result is used to compute the orbit-averaged flux of energy and angular momentum at Newtonian order, which means relative 1PN order beyond the leading-order dipolar radiation of scalar-tensor theories. The secular evolution of the orbital elements is then computed at 1PN order. At leading order, the closed form "Peters and Mathews" relation between the semi-major axis $a$ and the eccentricity $e$ is found to be independent of any scalar-tensor parameter, and is given by $a \propto e^{4/3}/(1-e^2)$. Finally, the waveform is obtained at Newtonian order in the form of a spherical harmonic mode decomposition, extending to eccentric orbits the results obtained in arXiv:2201.10924.

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arXiv2023

Gravitational waves from compact binaries to the fourth post-Newtonian order

The precise knowledge of the gravitational phase evolution of compact binaries is crucial to the data analysis for gravitational waves. Until recently, it was known analytically (for non-spinning systems) up to the 3.5 post-Newtonian (PN) order, i.e. up to the $(v/c)^7$ correction beyond the leading order quadrupole formula. Using a PN-multipolar-post-Minkowskian algorithm, we have pushed the accuracy to the next 4PN level. This derivation involved challenging technical issues, due to the appearance of non-physical divergences, which have to be properly regularized, as well as effects of non-linear multipole interactions.

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arXiv2023

Gravitational Wave Flux and Quadrupole Modes from Quasi-Circular Non-Spinning Compact Binaries to the Fourth Post-Newtonian Order

This article provides the details on the technical derivation of the gravitational waveform and total gravitational-wave energy flux of non-spinning compact binary systems to the 4PN (fourth post-Newtonian) order beyond the Einstein quadrupole formula. In particular: (i) we overview the link between the radiative multipole moments measured at infinity and the source moments in the framework of dimensional regularization; (ii) we compute special corrections to the source moments due to "infrared" commutators arising at the 4PN order; (iii) we derive a "post-adiabatic" correction needed to evaluate the tail integral with 2.5PN relative precision; (iv) we discuss the relation between the binary's orbital frequency in quasi-circular orbit and the gravitational-wave frequency measured at infinity; (v) we compute the hereditary effects at the 4PN order, including those coming from the recently derived tails-of-memory; and (vi) we describe the various tests we have performed to ensure the correctness of the results. Those results are collected in an ancillary file.

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arXiv2023

Gravitational-Wave Phasing of Quasi-Circular Compact Binary Systems to the Fourth-and-a-Half post-Newtonian Order

The inspiral phase of gravitational waves emitted by spinless compact binary systems is derived through the fourth-and-a-half post-Newtonian (4.5PN) order beyond quadrupole radiation, and the leading amplitude mode ($\ell$, m) = (2, 2) is obtained at 4PN order. We also provide the radiated flux, as well as the phase in the stationary phase approximation. Rough numerical estimates for the contribution of each PN order are provided for typical systems observed by current and future gravitational wave detectors.

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arXiv2023

Gravitational-wave tails of memory

Gravitational-wave tails are linear waves that backscatter on the curvature of space-time generated by the total mass-energy of the source. The non-linear memory effect arises from gravitational waves sourced by the stress-energy distribution of linear waves themselves. These two effects are due to quadratic multipolar interactions (mass-quadrupole and quadrupole-quadrupole) and are well known. Also known are the tails generated by tails themselves (cubic "tails-of-tails") and the tails generated by tails-of-tails or vice versa (quartic "tails-of-tails-of-tails"). In this work, we focus on the cubic "tails-of-memory" corresponding to the mass-quadrupole-quadrupole interaction, as well as the "spin-quadrupole tails", which are due to the cubic interaction between the mass, the total angular momentum and the quadrupole. The tails-of-memory and the spin-quadrupole tails contribute to the asymptotic waveform at the fourth-post-Newtonian (4PN) order beyond quadrupolar radiation.

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arXiv2022

The Quadrupole Moment of Compact Binaries to the Fourth post-Newtonian Order: Relating the Harmonic and Radiative Metrics

Motivated by the completion of the fourth post-Newtonian (4PN) gravitational-wave generation from compact binary systems, we analyze and contrast different constructions of the metric outside an isolated system, using post-Minkowskian expansions. The metric in "harmonic" coordinates has been investigated previously, in particular to compute tails and memory effects. However, it is plagued by powers of the logarithm of the radial distance $r$ when $r\to\infty$ (with $t-r/c=$ const). As a result, the tedious computation of the "tail-of-memory" effect, which enters the gravitational-wave flux at 4PN order, is more efficiently performed in the so-called "radiative" coordinates, which admit a (Bondi-type) expansion at infinity in simple powers of $r^{-1}$, without any logarithms. Here we consider a particular construction, performed order by order in the post-Minkowskian expansion, which directly yields a metric in radiative coordinates. We relate both constructions, and prove that they are physically equivalent as soon as a relation between the "canonical" moments which parametrize the radiative metric, and those parametrizing the harmonic metric, is verified. We provide the appropriate relation for the mass quadrupole moment at 4PN order, which will be crucial when deriving the "tail-of-memory" contribution to the gravitational flux.

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arXiv2022

UGR tests with atomic clocks and atom interferometers

Atomic interference experiments test the universality of the coupling between matter-energy and gravity at different spacetime points, thus being in principle able to probe possible violations of the universality of the gravitational redshift (UGR). In this contribution, we introduce a UGR violation model and then discuss UGR tests performed by atomic clocks and atom interferometers on the same footing. We present a large class of atom-interferometric geometries which are sensitive to violations of UGR.

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arXiv2022

Gravitational waves in scalar-tensor theory to one-and-a-half post-Newtonian order

We compute the gravitational waves generated by compact binary systems in a class of massless scalar-tensor (ST) theories to the 1.5 post-Newtonian (1.5PN) order beyond the standard quadrupole radiation in general relativity (GR). Using and adapting to ST theories the multipolar-post-Minkowskian and post-Newtonian formalisms originally defined in GR, we obtain the tail and non-linear memory terms associated with the dipole radiation in ST theory. The multipole moments and GW flux of compact binaries are derived for general orbits including the new 1.5PN contribution, and comparison is made with previous results in the literature. In the case of quasi-circular orbits, we present ready-to-use templates for the data analysis of detectors, and for the first time the scalar GW modes for comparisons with numerical relativity results.

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