Preprint

PUBDB-2022-00137

http://join2-wiki.gsi.de/foswiki/pub/Main/Artwork/join2_logo100x88.png The Quadrupole Moment of Compact Binaries to the Fourth post-Newtonian Order: I. Non-Locality in Time and Infra-Red Divergencies

Larrouturou, F. (Corresponding author)DESY* ; Henry, Q. ; Blanchet, L. ; Faye, G.

2022

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Please use a persistent id in citations: doi:10.3204/PUBDB-2022-00137

Report No.: DESY-22-005; arXiv:2110.02240

Abstract: 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 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 radiative type quadrupole moment measured at future null infinity.

Note: 24 pages, no figures

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Contributing Institute(s):

1. Theoretische Gravitationswellenastrophys (Z_THAT)

Research Program(s):

1. 611 - Fundamental Particles and Forces (POF4-611) (POF4-611)
2. LHCtoLISA - Precision Gravity: From the LHC to LISA (817791) (817791)

Experiment(s):

1. No specific instrument

Appears in the scientific report 2022

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Database coverage:
; ; Published

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Linked articles:

http://join2-wiki.gsi.de/foswiki/pub/Main/Artwork/join2_logo100x88.png Preprint Larrouturou, F. (Corresponding author)DESY* ; Blanchet, L. ; Henry, Q. ; Faye, G.
The Quadrupole Moment of Compact Binaries to the Fourth post-Newtonian Order: II. Dimensional Regularization and Renormalization
[10.3204/PUBDB-2022-00139]     Files  Fulltext by arXiv.org BibTeX | EndNote: XML, Text | RIS

http://join2-wiki.gsi.de/foswiki/pub/Main/Artwork/join2_logo100x88.png Journal Article Larrouturou, F. (Corresponding author)Extern*DESY* ; Henry, Q. ; Blanchet, L. ; Faye, G.
The Quadrupole Moment of Compact Binaries to the Fourth post-Newtonian Order: I. Non-Locality in Time and Infra-Red Divergencies
Classical and quantum gravity 39, 115007 (2022) [10.1088/1361-6382/ac5762]2022     Files  Fulltext by arXiv.org BibTeX | EndNote: XML, Text | RIS

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