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

Abstract

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.

40 pages, 1 table

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• Tidal effects in the total flux and waveform in massless scalar-tensor theories to, respectively, relative 2PN and 1.5PN orders
• General Fourier expansion of post-Newtonian binary dynamics based on a quasi-Keplerian framework
• Gravitational radiation reaction for compact binary systems at the fourth-and-a-half post-Newtonian order in harmonic coordinates
• Fixing the center-of-mass frame of numerical relativity waveforms using the post-Newtonian center-of-mass charge