Gravitational radiation reaction in the equations of motion of compact binaries to 3.5 post-Newtonian order

TL;DR

This paper calculates the 3.5 post-Newtonian order gravitational radiation reaction force on compact binary systems, improving the precision of orbital motion models for gravitational wave predictions.

Contribution

It introduces a direct post-Newtonian iteration method for deriving the radiation reaction force at 3.5PN order, extending previous work beyond the dominant effect.

Findings

Derived the 3.5PN acceleration term in harmonic coordinates.

Confirmed agreement with previous results in the center-of-mass frame.

Provided a formalism applicable to point-particle binary systems.

Abstract

We compute the radiation reaction force on the orbital motion of compact binaries to the 3.5 post-Newtonian (3.5PN) approximation, i.e. one PN order beyond the dominant effect. The method is based on a direct PN iteration of the near-zone metric and equations of motion of an extended isolated system, using appropriate ``asymptotically matched'' flat-space-time retarded potentials. The formalism is subsequently applied to binary systems of point particles, with the help of the Hadamard self-field regularisation. Our result is the 3.5PN acceleration term in a general harmonic coordinate frame. Restricting the expression to the centre-of-mass frame, we find perfect agreement with the result derived in a class of coordinate systems by Iyer and Will using the energy and angular momentum balance equations.