30 research outputs found
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.Comment: Contribution to the 2022 Gravitation session of the 56th Rencontres
de Moriond. 4 page
Gravitational-wave tails of memory at 4PN order
We study a novel cubic nonlinear effect, the tails-of-memory, which consist
of a combination of the tail effect (backscattering of linear gravitational
waves against the curvature of spacetime generated by the source) and the
memory effect (due to reradiation of gravitational waves by linear
gravitational waves themselves). Our final result is consistent with a
straightforward direct computation of the memory effect, but also involves many
non-trivial tail-like terms.Comment: Contribution to the 2023 Gravitation session of the 57th Rencontres
de Moriond. 5 pages, 1 figur
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.Comment: 40 page, 1 figure, 1 table and 2 ancillary file
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 when (with 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 , 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.Comment: Updated a reference: Blanchet, Faye & Larrouturou 2022 in CQ
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 (, 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.Comment: 9 pages, 1 table. v2: reference of the companion paper updated. v3:
post-referee version, typo corrected in Eq. (9
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.Comment: 32 pages, no figure. v2: reference of the companion letter updated.
v3: post-referee versio
Gravitational radiation of compact binary systems in general relativity and in scalar-tensor theories
Nous amĂ©liorons les prĂ©dictions thĂ©oriques analytiques concernant les ondes gravitationnelles (OG) Ă©mises par des systĂšmes binaires compacts d'Ă©toiles Ă neutrons ou de trous noirs pendant la phase spiralante prĂ©cĂ©dant la coalescence, Ă la fois en relativitĂ© gĂ©nĂ©rale (RG) et dans une classe de thĂ©ories tenseur-scalaire (TS). Nous utilisons un formalisme qui combine le dĂ©veloppement multipolaire post-minkowskien (MPM) de la mĂ©trique dans le vide extĂ©rieur Ă un systĂšme de matiĂšre isolĂ©, avec le dĂ©veloppement post-newtonien (PN) pour des petites vitesses orbitales (v << c) et des champs gravitationnels faibles. En RG, nous calculons les modes (l,m) de la forme d'OG Ă l'ordre 4PN, en (v/c)^8 au-delĂ de l'ordre dominant, ainsi que la phase et le flux d'Ă©nergie Ă 4.5PN. Pour cela, nous Ă©tudions de nouveaux termes non-linĂ©aires dans la propagation des OG. Le principal effet est le "sillage de mĂ©moire", qui est dĂ» aux effets combinĂ©s (i) des sillages d'OG, c'est-Ă -dire de la diffusion des OG sur la courbure de l'espace-temps gĂ©nĂ©rĂ©e par la masse totale de la binaire; et (ii) de l'effet de mĂ©moire, dĂ» au rayonnement gravitationnel engendrĂ© par les OG elles-mĂȘmes. Ce calcul a nĂ©cessitĂ© l'implĂ©mentation d'une construction MPM dite "radiative" de la mĂ©trique du vide extĂ©rieur, qui Ă©limine de la zone lointaine les logarithmes en la coordonnĂ©e radiale qui apparaissent dans la construction en coordonnĂ©es harmoniques standard. Dans les thĂ©ories TS, nous adaptons le cadre PN-MPM Ă l'ordre 1.5PN (c'est-Ă -dire 2.5PN au-delĂ du rayonnement dipolaire dominant dans les thĂ©ories TS). Nous obtenons ainsi le flux, la phase et les modes (l,m) des champs scalaires et tensoriels Ă l'ordre 1.5PN pour des orbites circulaires, et corrigeons une erreur dans la littĂ©rature pour les orbites gĂ©nĂ©rales.We improve analytical theoretical predictions for gravitational waves (GWs) emitted by compact binary systems of neutron stars and black holes during the inspiraling phase preceding merger, both in general relativity (GR) and in a class of scalar-tensor (ST) theories. We resort to a formalism that combines the multipolar post-Minkowskian (MPM) expansion of the vacuum metric exterior to an isolated matter system and the post-Newtonian (PN) expansion in small orbital velocities (v << c) and weak gravitational fields. In GR, we compute the (l,m) modes of the GW up to 4PN order, i.e. (v/c)^8 beyond leading order, as well as the phase and energy flux up to 4.5PN order. For this, we study novel nonlinear terms in the propagation of GWs. The main effect is the "tail of memory", which is due to the combined effects of (i) GW tails, i.e. the backscattering of GWs against the spacetime curvature generated by the total mass of the binary; and (ii) the memory effect, due to the reradiation of GWs by GWs themselves. This computation required implementing the so-called "radiative" MPM construction of the exterior vacuum metric, which removes the far-zone logarithms in the radial coordinate that appear in the standard construction in harmonic coordinates. In ST theories, we adapt the PN-MPM framework at 1.5PN order (i.e. 2.5PN beyond the leading dipolar radiation of ST theories). We thus obtain the flux, phase and (l,m) modes of the scalar and tensor fields at 1.5PN order for circular orbits, and correct a mistake in the literature for general orbits
Gravitational waves in scalar-tensor theory to one-and-a-half post-Newtonian order
International audienceWe 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
Rayonnement gravitationnel des systÚmes binaires compacts en relativité générale et dans les théories tenseur-scalaire
We improve analytical theoretical predictions for gravitational waves (GWs) emitted by compact binary systems of neutron stars and black holes during the inspiraling phase preceding merger, both in general relativity (GR) and in a class of scalar-tensor (ST) theories. We resort to a formalism that combines the multipolar post-Minkowskian (MPM) expansion of the vacuum metric exterior to an isolated matter system and the post-Newtonian (PN) expansion in small orbital velocities (v << c) and weak gravitational fields. In GR, we compute the (l,m) modes of the GW up to 4PN order, i.e. (v/c)^8 beyond leading order, as well as the phase and energy flux up to 4.5PN order. For this, we study novel nonlinear terms in the propagation of GWs. The main effect is the "tail of memory", which is due to the combined effects of (i) GW tails, i.e. the backscattering of GWs against the spacetime curvature generated by the total mass of the binary; and (ii) the memory effect, due to the reradiation of GWs by GWs themselves. This computation required implementing the so-called "radiative" MPM construction of the exterior vacuum metric, which removes the far-zone logarithms in the radial coordinate that appear in the standard construction in harmonic coordinates. In ST theories, we adapt the PN-MPM framework at 1.5PN order (i.e. 2.5PN beyond the leading dipolar radiation of ST theories). We thus obtain the flux, phase and (l,m) modes of the scalar and tensor fields at 1.5PN order for circular orbits, and correct a mistake in the literature for general orbits.Nous amĂ©liorons les prĂ©dictions thĂ©oriques analytiques concernant les ondes gravitationnelles (OG) Ă©mises par des systĂšmes binaires compacts d'Ă©toiles Ă neutrons ou de trous noirs pendant la phase spiralante prĂ©cĂ©dant la coalescence, Ă la fois en relativitĂ© gĂ©nĂ©rale (RG) et dans une classe de thĂ©ories tenseur-scalaire (TS). Nous utilisons un formalisme qui combine le dĂ©veloppement multipolaire post-minkowskien (MPM) de la mĂ©trique dans le vide extĂ©rieur Ă un systĂšme de matiĂšre isolĂ©, avec le dĂ©veloppement post-newtonien (PN) pour des petites vitesses orbitales (v << c) et des champs gravitationnels faibles. En RG, nous calculons les modes (l,m) de la forme d'OG Ă l'ordre 4PN, en (v/c)^8 au-delĂ de l'ordre dominant, ainsi que la phase et le flux d'Ă©nergie Ă 4.5PN. Pour cela, nous Ă©tudions de nouveaux termes non-linĂ©aires dans la propagation des OG. Le principal effet est le "sillage de mĂ©moire", qui est dĂ» aux effets combinĂ©s (i) des sillages d'OG, c'est-Ă -dire de la diffusion des OG sur la courbure de l'espace-temps gĂ©nĂ©rĂ©e par la masse totale de la binaire; et (ii) de l'effet de mĂ©moire, dĂ» au rayonnement gravitationnel engendrĂ© par les OG elles-mĂȘmes. Ce calcul a nĂ©cessitĂ© l'implĂ©mentation d'une construction MPM dite "radiative" de la mĂ©trique du vide extĂ©rieur, qui Ă©limine de la zone lointaine les logarithmes en la coordonnĂ©e radiale qui apparaissent dans la construction en coordonnĂ©es harmoniques standard. Dans les thĂ©ories TS, nous adaptons le cadre PN-MPM Ă l'ordre 1.5PN (c'est-Ă -dire 2.5PN au-delĂ du rayonnement dipolaire dominant dans les thĂ©ories TS). Nous obtenons ainsi le flux, la phase et les modes (l,m) des champs scalaires et tensoriels Ă l'ordre 1.5PN pour des orbites circulaires, et corrigeons une erreur dans la littĂ©rature pour les orbites gĂ©nĂ©rales
Rayonnement gravitationnel des systÚmes binaires compacts en relativité générale et dans les théories tenseur-scalaire
We improve analytical theoretical predictions for gravitational waves (GWs) emitted by compact binary systems of neutron stars and black holes during the inspiraling phase preceding merger, both in general relativity (GR) and in a class of scalar-tensor (ST) theories. We resort to a formalism that combines the multipolar post-Minkowskian (MPM) expansion of the vacuum metric exterior to an isolated matter system and the post-Newtonian (PN) expansion in small orbital velocities (v << c) and weak gravitational fields. In GR, we compute the (l,m) modes of the GW up to 4PN order, i.e. (v/c)^8 beyond leading order, as well as the phase and energy flux up to 4.5PN order. For this, we study novel nonlinear terms in the propagation of GWs. The main effect is the "tail of memory", which is due to the combined effects of (i) GW tails, i.e. the backscattering of GWs against the spacetime curvature generated by the total mass of the binary; and (ii) the memory effect, due to the reradiation of GWs by GWs themselves. This computation required implementing the so-called "radiative" MPM construction of the exterior vacuum metric, which removes the far-zone logarithms in the radial coordinate that appear in the standard construction in harmonic coordinates. In ST theories, we adapt the PN-MPM framework at 1.5PN order (i.e. 2.5PN beyond the leading dipolar radiation of ST theories). We thus obtain the flux, phase and (l,m) modes of the scalar and tensor fields at 1.5PN order for circular orbits, and correct a mistake in the literature for general orbits.Nous amĂ©liorons les prĂ©dictions thĂ©oriques analytiques concernant les ondes gravitationnelles (OG) Ă©mises par des systĂšmes binaires compacts d'Ă©toiles Ă neutrons ou de trous noirs pendant la phase spiralante prĂ©cĂ©dant la coalescence, Ă la fois en relativitĂ© gĂ©nĂ©rale (RG) et dans une classe de thĂ©ories tenseur-scalaire (TS). Nous utilisons un formalisme qui combine le dĂ©veloppement multipolaire post-minkowskien (MPM) de la mĂ©trique dans le vide extĂ©rieur Ă un systĂšme de matiĂšre isolĂ©, avec le dĂ©veloppement post-newtonien (PN) pour des petites vitesses orbitales (v << c) et des champs gravitationnels faibles. En RG, nous calculons les modes (l,m) de la forme d'OG Ă l'ordre 4PN, en (v/c)^8 au-delĂ de l'ordre dominant, ainsi que la phase et le flux d'Ă©nergie Ă 4.5PN. Pour cela, nous Ă©tudions de nouveaux termes non-linĂ©aires dans la propagation des OG. Le principal effet est le "sillage de mĂ©moire", qui est dĂ» aux effets combinĂ©s (i) des sillages d'OG, c'est-Ă -dire de la diffusion des OG sur la courbure de l'espace-temps gĂ©nĂ©rĂ©e par la masse totale de la binaire; et (ii) de l'effet de mĂ©moire, dĂ» au rayonnement gravitationnel engendrĂ© par les OG elles-mĂȘmes. Ce calcul a nĂ©cessitĂ© l'implĂ©mentation d'une construction MPM dite "radiative" de la mĂ©trique du vide extĂ©rieur, qui Ă©limine de la zone lointaine les logarithmes en la coordonnĂ©e radiale qui apparaissent dans la construction en coordonnĂ©es harmoniques standard. Dans les thĂ©ories TS, nous adaptons le cadre PN-MPM Ă l'ordre 1.5PN (c'est-Ă -dire 2.5PN au-delĂ du rayonnement dipolaire dominant dans les thĂ©ories TS). Nous obtenons ainsi le flux, la phase et les modes (l,m) des champs scalaires et tensoriels Ă l'ordre 1.5PN pour des orbites circulaires, et corrigeons une erreur dans la littĂ©rature pour les orbites gĂ©nĂ©rales