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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, including spin-spin effects. In particularwe determine the effects of radiation-reaction coupled to spin-spin effects onthe two-body equations of motion, and on the evolution of the spins. We findthat radiation damping causes a 3.5PN order, spin-spin induced precession ofthe individual spins. This contrasts with the case of spin-orbit coupling,where there is no effect on the spins at 3.5PN order. Employing the equationsof motion and of spin precession, we verify that the loss of total energy andtotal angular momentum induced by spin-spin effects precisely balances theradiative flux of those quantities calculated by Kidder et al.Comment: 10 pages, coincides with published versio

physical review. d. particles, fields, gravitation, and cosmology/physical review. d, particles, fields, gravitation, and cosmology

Post-Newtonian gravitational radiation and equations of motion via direct integration of the relaxed Einstein equations. IV. Radiation reaction for binary systems with spin-spin coupling