Preprint

PUBDB-2022-00139

http://join2-wiki.gsi.de/foswiki/pub/Main/Artwork/join2_logo100x88.png The Quadrupole Moment of Compact Binaries to the Fourth post-Newtonian Order: II. Dimensional Regularization and Renormalization

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

2022

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Please use a persistent id in citations: doi:10.3204/PUBDB-2022-00139

Report No.: DESY-22-006; arXiv:2110.02243

Abstract: The regularization and renormalization of the radiative mass-type quadrupole moment of inspiralling compact binaries (without spins) is investigated at the fourth post-Newtonian (4PN) approximation of general relativity. As clear from the conservative 4PN equations of motion, a dimensional regularization has to be implemented in order to properly treat the non-linear interactions experienced by gravitational waves during their propagation toward future null infinity. By implementing such procedure, we show that the poles coming from the source moment (computed in a companion paper) are exactly cancelled in the radiative moment, as expected for a physical quantity. We thus define and obtain a 'renormalized' source quadrupole, three-dimensional by nature, which is an important step towards the computation of the gravitational-wave flux with 4PN accuracy. Furthermore, we explicitly prove the equivalence between the dimensional regularization and the previously used Hadamard partie finie scheme up to the 3PN order.

Keyword(s): regularization: dimensional ; binary: compact ; interaction: nonlinear ; gravitational radiation: flux ; dimension: 3 ; moment ; renormalization ; general relativity ; pole ; field equations ; propagation ; conservation law ; spin ; multipole ; asymptotic expansion ; higher-order: 4 ; Hadamard state

Note: 25 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 Journal Article Larrouturou, F. (Corresponding author)Extern*DESY* ; Blanchet, L. ; Henry, Q. ; Faye, G.
The Quadrupole Moment of Compact Binaries to the Fourth post-Newtonian Order: II. Dimensional Regularization and Renormalization
Classical and quantum gravity 39(11), 115008 (2022) [10.1088/1361-6382/ac5ba0]2022     Files  Fulltext by arXiv.org BibTeX | EndNote: XML, Text | RIS

http://join2-wiki.gsi.de/foswiki/pub/Main/Artwork/join2_logo100x88.png Preprint Larrouturou, F. (Corresponding author)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
[10.3204/PUBDB-2022-00137]     Files  Fulltext by arXiv.org BibTeX | EndNote: XML, Text | RIS

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