The Quadrupole Moment of Compact Binaries to the Fourth post-Newtonian Order: II. Dimensional Regularization and Renormalization

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

doi:10.1088/1361-6382/ac5ba0

Journal Article

PUBDB-2022-03179

The Quadrupole Moment of Compact Binaries to the Fourth post-Newtonian Order: II. Dimensional Regularization and Renormalization

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

2022
IOP Publ. Bristol

Classical and quantum gravity 39(11), 115008 (2022) [10.1088/1361-6382/ac5ba0]

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Please use a persistent id in citations: doi:10.1088/1361-6382/ac5ba0 doi:10.3204/PUBDB-2022-03179

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 ; post-Newtonian approximation ; gravitational waves ; black holes ; neutron stars

Classification:

ddc:530

Note: 25 pages, no figures

Contributing Institute(s):

Theoretische Gravitationswellenastrophys (Z_THAT)

Research Program(s):

Experiment(s):

No specific instrument

Appears in the scientific report 2022

Database coverage:
Medline

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