Application of energy and angular momentum balance to gravitational radiation reaction for binary systems with spin-orbit coupling

TL;DR

This work addresses gravitational radiation reaction for binaries with spin-orbit coupling at order $O((v/c)^7)$ beyond Newtonian gravity. The authors apply energy and angular momentum balance, using spin-orbit fluxes to constrain the $3.5$PN spin-orbit corrections to the two-body equations of motion, and show that $50$ of $62$ arbitrary coefficients are fixed, leaving $12$ that map to gauge freedom. A particular gauge choice yields $3.5$PN spin-orbit terms in agreement with earlier first-principles calculations, and the study confirms that spins' magnitudes are not altered by radiation reaction at this order. The results clarify the role of gauge freedom in high-order PN radiation reaction and enable systematic waveform modeling for spinning binaries, with planned extensions to spin-spin interactions.

Abstract

We study gravitational radiation reaction in the equations of motion for binary systems with spin-orbit coupling, at order (v/c)^7 beyond Newtonian gravity, or O(v/c)^2 beyond the leading radiation reaction effects for non-spinning bodies. We use expressions for the energy and angular momentum flux at infinity that include spin-orbit corrections, together with an assumption of energy and angular momentum balance, to derive equations of motion that are valid for general orbits and for a class of coordinate gauges. We show that the equations of motion are compatible with those derived earlier by a direct calculation.