Post-Newtonian gravitational radiation and equations of motion via direct integration of the relaxed Einstein equations. III. Radiation reaction for binary systems with spinning bodies

TL;DR

The paper addresses the problem of modeling gravitational radiation reaction in binary systems with spinning bodies within the post-Newtonian framework. It advances by applying direct integration of the relaxed Einstein equations to derive 2.5PN and 3.5PN radiation-reaction terms, including spin-orbit couplings, and presents instantaneous equations of motion and spin precession up to 3.5PN order. The key findings are that radiation reaction affects the orbital dynamics via spin-orbit terms at 3.5PN while leaving the spins themselves unchanged, and that the orbital energy and angular momentum losses balance the corresponding gravitational-wave flux as calculated by prior work (Kidder et al.). This work provides a practical, non-averaged set of equations for evolving inspiraling binaries with spins, forming a basis for high-precision waveform modeling and parameter estimation in gravitational-wave astronomy.

Abstract

Using post-Newtonian equations of motion for fluid bodies that include radiation-reaction terms at 2.5 and 3.5 post-Newtonian (PN) order (O[(v/c)^5] and O[(v/c)^7] beyond Newtonian order), we derive the equations of motion for binary systems with spinning bodies. In particular we determine the effects of radiation-reaction coupled to spin-orbit effects on the two-body equations of motion, and on the evolution of the spins. For a suitable definition of spin, we reproduce the standard equations of motion and spin-precession at the first post-Newtonian order. At 3.5PN order, we determine the spin-orbit induced reaction effects on the orbital motion, but we find that radiation damping has no effect on either the magnitude or the direction of the spins. Using the equations of motion, we find that the loss of total energy and total angular momentum induced by spin-orbit effects precisely balances the radiative flux of those quantities calculated by Kidder et al. The equations of motion may be useful for evolving inspiraling orbits of compact spinning binaries.