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Gravitational radiation reaction for compact binary systems at the fourth-and-a-half post-Newtonian order

Gravitational radiation reaction for compact binary systems at the fourth-and-a-half post-Newtonian order
Gravitational radiation reaction for compact binary systems at the fourth-and-a-half post-Newtonian order
We compute the gravitational radiation-reaction (RR) force on a compact binary source at the fourth-and-a-half post-Newtonian (4.5PN) order of general relativity, i.e. 2PN order beyond the leading 2.5PN radiation reaction. The calculation is valid for general orbits in a general frame, but in a particular coordinate system which is an extension of the Burke-Thorne coordinate system at the lowest order. With the RR acceleration, we derive (from first principles) the flux-balance laws associated with the energy, the angular and linear momenta, and the center-of-mass (CM) position, in a general frame and up to 4.5PN order. Restricting our attention to the frame of the center of mass, we point out that the equations of motion (EOM) acquire a non-local-in-time contribution at the 4.5PN order, made of the integrated flux of linear momentum (responsible for the recoil of the source) together with the instantaneous flux of CM position. The non-local contribution was overlooked in the past literature, which assumed locality of the RR force in the center of mass frame at 4.5PN order. We discuss the consequences of this non-local effect and obtain consistent non-local EOM and flux balance laws at 4.5PN order in the CM frame.
center-of-mass frame, equations of motion, flux-balance laws, gravitational kick, gravitational radiation reaction, gravitational recoil, post-Newtonian
0264-9381
Blanchet, Luc
d208bbd8-6eb0-4da8-adb2-e5e46afd2596
Faye, Guillaume
462a7e27-ec6a-45d3-aaa7-37a2af14c0ae
Trestini, David
f72ecc41-21fa-453b-8209-01a7ab746b89
Blanchet, Luc
d208bbd8-6eb0-4da8-adb2-e5e46afd2596
Faye, Guillaume
462a7e27-ec6a-45d3-aaa7-37a2af14c0ae
Trestini, David
f72ecc41-21fa-453b-8209-01a7ab746b89

Blanchet, Luc, Faye, Guillaume and Trestini, David (2025) Gravitational radiation reaction for compact binary systems at the fourth-and-a-half post-Newtonian order. Classical and Quantum Gravity, 42 (6), [065015]. (doi:10.1088/1361-6382/adac9d).

Record type: Article

Abstract

We compute the gravitational radiation-reaction (RR) force on a compact binary source at the fourth-and-a-half post-Newtonian (4.5PN) order of general relativity, i.e. 2PN order beyond the leading 2.5PN radiation reaction. The calculation is valid for general orbits in a general frame, but in a particular coordinate system which is an extension of the Burke-Thorne coordinate system at the lowest order. With the RR acceleration, we derive (from first principles) the flux-balance laws associated with the energy, the angular and linear momenta, and the center-of-mass (CM) position, in a general frame and up to 4.5PN order. Restricting our attention to the frame of the center of mass, we point out that the equations of motion (EOM) acquire a non-local-in-time contribution at the 4.5PN order, made of the integrated flux of linear momentum (responsible for the recoil of the source) together with the instantaneous flux of CM position. The non-local contribution was overlooked in the past literature, which assumed locality of the RR force in the center of mass frame at 4.5PN order. We discuss the consequences of this non-local effect and obtain consistent non-local EOM and flux balance laws at 4.5PN order in the CM frame.

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Accepted/In Press date: 25 January 2025
Published date: 4 March 2025
Keywords: center-of-mass frame, equations of motion, flux-balance laws, gravitational kick, gravitational radiation reaction, gravitational recoil, post-Newtonian

Identifiers

Local EPrints ID: 504208
URI: http://eprints.soton.ac.uk/id/eprint/504208
ISSN: 0264-9381
PURE UUID: efeba367-5cdd-4c4e-98e9-566e0a62b492
ORCID for David Trestini: ORCID iD orcid.org/0000-0002-4140-0591

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Date deposited: 29 Aug 2025 16:48
Last modified: 30 Aug 2025 02:17

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Contributors

Author: Luc Blanchet
Author: Guillaume Faye
Author: David Trestini ORCID iD

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