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

摘要

Using post-Newtonian equations of motion for fluid bodies that includeradiation-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 forbinary systems with spinning bodies. In particular we determine the effects ofradiation-reaction coupled to spin-orbit effects on the two-body equations ofmotion, 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 firstpost-Newtonian order. At 3.5PN order, we determine the spin-orbit inducedreaction effects on the orbital motion, but we find that radiation damping hasno effect on either the magnitude or the direction of the spins. Using theequations of motion, we find that the loss of total energy and total angularmomentum induced by spin-orbit effects precisely balances the radiative flux ofthose quantities calculated by Kidder et al. The equations of motion may beuseful for evolving inspiraling orbits of compact spinning binaries.