Gravitational radiation reaction in the Newtonian limit

The asymptotic approximation scheme based on the theory of the Newtonian limit developed in the preceding paper is applied to the gravitational radiation-reaction problem. All divergences encountered in previous approaches disappear: For any the asymptotic approximation is finite to all orders we have calculated, even beyond radiation-reaction order. This is because the divergent terms in previous work were misordered, and make finite contributions to coefficients of lower-order terms in the asymptotic expansion. The logarithmic divergences, in particular, turn up as an 10 ln term in the asymptotic expansion (i.e., between 2.5 and 3 post-Newtonian order) which shows that the relativistic sequence is not C at =0. This does not, however, affect the asymptotic convergence of the approximation. The radiation-reaction terms are used to calculate the period shortening of a nearly-Newtonian binary system directly from the equations of motion, avoiding the well-known difficulties associated with energy in general relativity. It is proved that the prediction derived from the standard quadrupole formula applies in the Newtonian limit. It is also shown that random data for the initial gravitational wave field do not affect the calculation of radiation reaction, even if their amplitude is of first post-Newtonian order.