Second post-Newtonian gravitational radiation reaction for two-body systems: Nonspinning bodies

TL;DR

This paper derives the second post-Newtonian order gravitational radiation reaction force for nonspinning two-body systems, extending previous models to include higher-order effects for more accurate orbital dynamics.

Contribution

It introduces a 2PN accurate radiation reaction force beyond the quadrupole approximation, using a refined balance method applicable to general orbits and gauges.

Findings

Derived 2PN radiation reaction equations for inspiralling binaries.

Validated equations for circular and radial orbits.

Compared different construction methods for radiation reaction forces.

Abstract

Starting from the recently obtained 2PN accurate forms of the energy and angular momentum fluxes from inspiralling compact binaries, we deduce the gravitational radiation reaction to 2PN order beyond the quadrupole approximation - 4.5PN terms in the equation of motion - using the refined balance method proposed by Iyer and Will. We explore critically the features of their construction and illustrate them by contrast to other possible variants. The equations of motion are valid for general binary orbits and for a class of coordinate gauges. The limiting cases of circular orbits and radial infall are also discussed.