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

TL;DR

This work extends the refined balance approach of Iyer and Will to 4.5PN order to derive gravitational radiation-reaction terms for nonspinning two-body systems, using 2PN energy and angular momentum fluxes. The reactive acceleration is constructed with a general ansatz containing numerous gauge-related parameters, and the balance equations fix these terms up to a 12-parameter gauge freedom, with two redundancies arising in circular-orbit limits. The authors explicitly compute the 2.5PN and 3.5PN reactive terms and provide the full 4.5PN framework, including the corresponding energy and angular momentum ambiguities, and explore several variant schemes that test the robustness of the results. Special cases, notably quasi-circular inspiral and head-on infall, are treated to verify consistency with known results, demonstrating the practical utility of the 4.5PN reactive terms for high-precision waveform modeling and orbital evolution. The work also discusses gauge choices and the physical interpretation of arbitrariness, highlighting that while the balance formalism permits a broad class of solutions, the physically meaningful ones correspond to specific gauge selections and mass-nonlinearity structures.

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.