Gravitational radiation reaction for compact binary systems at the fourth-and-a-half post-Newtonian order
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arXiv
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| Format: | Preprint |
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2024
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| author | Blanchet, Luc Faye, Guillaume Trestini, David |
| author_facet | Blanchet, Luc Faye, Guillaume Trestini, David |
| contents | We compute the gravitational radiation-reaction 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 radiation-reaction acceleration, we derive (from first principles) the flux-balance laws associated with the energy, the angular and linear momenta, and the center-of-mass 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 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 center-of-mass position. The non-local contribution was overlooked in the past literature, which assumed locality of the radiation-reaction 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 equations of motion and flux balance laws at 4.5PN order in the center-of-mass frame. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2407_18295 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Gravitational radiation reaction for compact binary systems at the fourth-and-a-half post-Newtonian order Blanchet, Luc Faye, Guillaume Trestini, David General Relativity and Quantum Cosmology We compute the gravitational radiation-reaction 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 radiation-reaction acceleration, we derive (from first principles) the flux-balance laws associated with the energy, the angular and linear momenta, and the center-of-mass 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 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 center-of-mass position. The non-local contribution was overlooked in the past literature, which assumed locality of the radiation-reaction 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 equations of motion and flux balance laws at 4.5PN order in the center-of-mass frame. |
| title | Gravitational radiation reaction for compact binary systems at the fourth-and-a-half post-Newtonian order |
| topic | General Relativity and Quantum Cosmology |
| url | https://arxiv.org/abs/2407.18295 |