The quadrupole moment of compact binaries to the fourth post-Newtonian order: II. Dimensional regularization and renormalization

Larrouturou, François; Blanchet, Luc; Henry, Quentin; Faye, Guillaume

doi:10.1088/1361-6382/ac5ba0

Cited by 22 publications

(31 citation statements)

References 57 publications

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“…Thus, we treat those in the source moment with the Hadamard partie finie regularization and add the non-linear corrections due to tails and tails-of-tails as computed in 3 dimensions. This will be further investigated elsewhere [36].…”

Section: The Current Quadrupole Moment Of Compact Binariesmentioning

confidence: 94%

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The current-type quadrupole moment and gravitational-wave mode $(\ell,m)=(2,1)$ of compact binary systems at the third post-Newtonian order

Henry,

Faye,

Blanchet

2021

Preprint

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Up to the third post-Newtonian (3PN) order, we compute (i) the current-type quadrupole moment of (non-spinning) compact binary systems, as well as (ii) the corresponding gravitational-wave mode (2, 1) (constituting a 3.5PN correction in the waveform). Moreover, at this occasion, (iii) we recompute and confirm the previous calculation of the mass-type octupole moment to 3PN order. The ultra-violet (UV) divergences due to the point-like nature of the source are treated by means of dimensional regularization. This entails generalizing the definition of the irreducible mass and current multipole moments of an isolated PN source in d spatial dimensions. In particular, we find that the current type moment has the symmetry of a particular mixed Young tableau and that, in addition, there appears a third type of moment which is however inexistent in 3 spatial dimensions.

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Section: The Current Quadrupole Moment Of Compact Binariesmentioning

confidence: 94%

“…• However, the IR divergences are treated using the Hadamard partie finie procedure with regulator rB in 3 dimensions (see Ref. [36] for a justification of this point).…”

Section: The Current Quadrupole Moment Of Compact Binariesmentioning

confidence: 99%

The current-type quadrupole moment and gravitational-wave mode $(\ell,m)=(2,1)$ of compact binary systems at the third post-Newtonian order

Henry,

Faye,

Blanchet

2021

Preprint

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“…(3.3) in [8] and recalled in Eq. ( 2.3) of the follow-up paper [34]. In other words, S L ⋆ (t, r) is an elementary monopolar homogeneous solution of the d'Alembertian equation, parametrized by the moments…”

Section: Far Zone Expansion Of the Potentials In D Dimensionsmentioning

confidence: 99%

“…In the present paper and the next one [34], we complete the derivation of the 4PN source mass-quadrupole moment of compact binaries. More precisely, our goals are two-fold: 1.…”

Section: Introductionmentioning

confidence: 99%

“…We then perform the proper IR dimensional regularization for all the various categories of terms composing the quadrupole in Section III. The final result is presented in Section IV in the form of a pole followed by a finite part contribution, which will be the starting point for the final renormalization of the quadrupole in the next paper [34]. Appendix A present technical formulas generalizing the Riesz formula in d dimensions.…”

Section: Introductionmentioning

confidence: 99%

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The quadrupole moment of compact binaries to the fourth post-Newtonian order: I. Non-locality in time and infra-red divergencies

Larrouturou¹,

Henry²,

Blanchet³

et al. 2022

Class. Quantum Grav.

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With the aim of providing high accuracy post-Newtonian (PN) templates for the analysis of gravitational waves generated by compact binary systems, we complete the analytical derivation of the \textit{source type} mass quadrupole moment of compact binaries (without spins) at the fourth PN order of general relativity. Similarly to the case of the conservative 4PN equations of motion, we show that the quadrupole moment at that order contains a non-local (in time) contribution, arising from the tail-transported interaction entering the conservative part of the dynamics. Furthermore, we investigate the infra-red (IR) divergences of the quadrupole moment. In a previous work, this moment has been computed using a Hadamard partie finie procedure for the IR divergences, but the knowledge of the conservative equations of motion indicates that those divergences have to be dealt with by means of dimensional regularization. This work thus derives the difference between the two regularization schemes, which has to be added on top of the previous result. We show that unphysical IR poles start to appear at the 3PN order, and we determine all of these up to the 4PN order. In particular, the non-local tail term comes in along with a specific pole at the 4PN order. It will be proven in a companion paper that the poles in the source-type quadrupole are cancelled in the physical \textit{radiative type} quadrupole moment measured at future null infinity.

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Radiation-reaction in the Effective Field Theory approach to Post-Minkowskian dynamics

Kälin

Neef

Porto

2023

J. High Energ. Phys.

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We extend the Post-Minkowskian (PM) effective field theory (EFT) approach to incorporate conservative and dissipative radiation-reaction effects in a unified framework. This is achieved by implementing the Schwinger-Keldysh “in-in” formalism and separating conservative and non-conservative terms according to the formulation in [1], which we show promotes Feynman’s i0-prescription and cutting rules to a prominent role at the classical level. The resulting integrals, involving both Feynman and retarded propagators, can be bootstrapped to all orders in the velocity via differential equations with boundary conditions including potential and radiation modes. As a paradigmatic example we provide an ab initio derivation of the classical solution to the scattering problem in general relativity to $$ \mathcal{O} $$ O (G3). For the sake of completeness, we also reproduce the leading order radiation-reaction effects in classical electrodynamics.

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The quadrupole moment of compact binaries to the fourth post-Newtonian order: II. Dimensional regularization and renormalization

Cited by 22 publications

References 57 publications

The current-type quadrupole moment and gravitational-wave mode $(\ell,m)=(2,1)$ of compact binary systems at the third post-Newtonian order

The current-type quadrupole moment and gravitational-wave mode $(\ell,m)=(2,1)$ of compact binary systems at the third post-Newtonian order

The quadrupole moment of compact binaries to the fourth post-Newtonian order: I. Non-locality in time and infra-red divergencies

Radiation-reaction in the Effective Field Theory approach to Post-Minkowskian dynamics

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