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Le groupe de travail « Formes d'onde » du Groupement de Recherche « Ondes Gravitationnelles » s'intéresse à l'étude de la dynamique des sources astrophysiques de rayonnement gravitationnel (binaires d'objets compacts, supernovæ à effondrement de cœur, étoiles à neutrons, ...), à la génération des formes d'ondes, ainsi qu'aux méthodes d'approximation employées dans ce contexte (relativité numérique, théories des perturbations, modèles effectifs à un corps, ...).
Nous proposons un atelier qui aura lieu le 24 septembre prochain dans l'amphithéâtre de l'Institut d'Astrophysique de Paris. Les personnes intéressées sont invitées à s'inscrire dès maintenant.
Orateurs invités:
Organisateurs: Luc Blanchet, Guillaume Faye, Éric Gourgoulhon, Alexandre Le Tiec
In this talk, we will review applications of EFT approaches in perturbative analytical approaches in GR. Specifically, we will discuss the Post-Newtonian (PN) and the Post-Minkowskian (PM) worldline Effective Field Theory (EFT) formalisms. Finally, we will discuss possible avenues towards the application of these methods in the Self-Force expansion based on recent work.
The past three years have seen two 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)]. I will present the comparison of these results where we find excellent agreement for the total flux, showing consistency between the two calculations at all available PN and SF orders. I will also briefly discuss the prospects for improving the comparisons in the future.
This presentation will focus on the study of the effects of a violation of Lorentz invariance on the generation of gravitational waves by compact objects. The theoretical framework used for this study is a model inspired by the SME (Standard Model Extension) formalism for parameterizing certain violations of General Relativity, including Lorentz invariance in the gravitational sector. I will show that this theoretical framework of modified gravity remains sensitive to the Post-Minkowskian (PM) method of solving the wave equation, and discuss the first results obtained. This work will subsequently be used to establish alternative gravitational-wave patterns for the detections of the future LISA mission, with the aim of estimating constraints on the parameters linked to Lorentz violation.
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.
In general relativity, freely-falling test objects follow geodesics of the background spacetime in which they live. In a sense, this feature is a mere rephrasing of Einstein’s equivalence principle. In 1968, Brandon Carter showed that the geodesic motion of objects orbiting a Kerr black hole was integrable, in the sense of Hamiltonian mechanics, by discovering a fourth constant of motion that now bears his name. This “universality” of geodesic free fall is, however, but an approximation: In general, two different bodies will follow two distinct paths, depending on how they spin and deform. I will show how, and to which extent, Carter’s integrability can be extended from geodesics to the motion of extended bodies that can spin and deform.
The study of tidal effects between compact objects such as neutron stars is particularly promising to better understand their physics. Including these effects in our waveform models could allow us to probe their internal structure, but also possibly to distinguish signals coming from black holes, neutron stars or even more exotic objects. This will be of paramount importance when interpreting the multiple signals expected with the arrival of the third-generation gravitational wave detectors.
The tidal interaction affects both the dynamics and the gravitational wave emission processes of compacts binaries resulting in a change in the orbital phase and the gravitational wave amplitude that are directly observable.
In this talk, I will present how we completed the computation of gravitational-waveform amplitude modes using the the post-Newtonian-multipolar-post-Minkowskian formalism and wrote them in form suitable for effective-one-body template building.
I will discuss nonlinear corrections to the tidal deformability and Love numbers of compact objects in general relativity, with particular focus on the case of black holes.
Nonlinear effects in black hole perturbation theory may be important for describing a black hole ringdown, as suggested by recent works. I will describe a new class of "quadratic" quasi-normal modes at second order in perturbation theory. Remarkably, not only their frequency but also their amplitude is completely determined by the linear modes themselves. I will present how one can compute them using Leaver's algorithm. Quadratic modes could be used to improve ringdown models by adding nonlinear features without introducing any supplementary free parameter for data analysis purposes, or to test GR in the nonlinear regime.
Predicting gravitational waveforms and oscillation modes of hypermassive neutron stars is a scientific challenge to take up before the post-O5 era of the LVK collaboration detectors and the arrival of Einstein Telescope and Cosmic Explorer. In the talk I will present ROXAS, a spectral code dedicated to isolated neutron star evolution and its preliminary results.