Application of energy and angular momentum balance to gravitational radiation reaction for binary systems with spinning bodies

We study the gravitational radiation reaction in the equations of motion for binary systems with spinning bodies in the general theory of relativity. We use the post-Newtonian (PN) approximation to that theory, and work to 1PN order beyond the leading order effects of radiation reaction, i.e. to 3.5PN order beyond normal Newtonian gravity. We assume energy and angular momentum balance and use the post-Newtonian expressions for energy and angular momentum fluxes at infinity with spin-orbit and spin-spin contributions, to generate equations of motion with spin-orbit and spin-spin radiation reaction contributions. The resulting equations of motion are compatible with those derived earlier by direct calculations and are valid for general orbits and for a class of coordinate gauges. We show that the residual freedom of the undetermined coefficients in the spin-orbit equations of motion corresponds to the arbitrariness of gauge choice.