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

This paper derives post-Newtonian equations of motion for binary systems with spinning bodies, including radiation-reaction effects at high PN orders, and analyzes how spin influences orbital evolution and energy/angular momentum loss.

Contribution

It extends previous models by incorporating spin-orbit effects into radiation-reaction terms at 2.5 and 3.5PN orders, providing detailed equations for spinning binary dynamics.

Findings

Radiation-reaction effects coupled with spin-orbit interactions are derived.

Spin magnitude and direction are unaffected by radiation damping at 3.5PN order.

Energy and angular momentum loss due to spin-orbit effects match radiative flux calculations.

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.