Second post-Newtonian gravitational radiation reaction for two-body systems: Nonspinning bodies

Starting from the recently obtained post-post-Newtonian (2PN) accurate forms of the energy and angular momentum fluxes from inspiraling compact binaries, we deduce the gravitational radiation reaction to 2PN order beyond the quadrupole approximation-4.5PN terms in the equation of motion-using the refined balance method proposed by Iyer and Will. We explore critically the features of their construction and illustrate them by contrast with other possible variants. The equations of motion are valid for general binary orbits and for a class of coordinate gauges. The limiting cases of circular orbits and radial infall are also discussed.