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

TL;DR

This paper calculates the 4.5PN order gravitational radiation-reaction force for compact binaries, revealing a non-local-in-time contribution affecting equations of motion and flux laws, which was previously overlooked.

Contribution

It provides the first derivation of non-local-in-time effects at 4.5PN order in gravitational radiation reaction for binary systems.

Findings

Derived 4.5PN radiation-reaction force for general orbits.

Identified non-local-in-time contributions at 4.5PN order.

Established consistent flux-balance laws including non-local effects.

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.