GRAVITATIONAL-RADIATION REACTION

In this chapter, we consider the radiation reaction to the motion of a point-like particle of mass m and specific spin S traveling on a curv ed background. Assuming S = O(Gm) and Gm << L where L is the length sc ale of the background curvature, we divide the spacetime into two regi ons; the external region where the metric is approximated by the backg round metric plus perturbations due to a point-like particle and the i nternal region where the metric is approximated by that of a black hol e plus perturbations due to the tidal effect of the background curvatu re, and use the technique of the matched asymptotic expansion to const ruct an approximate metric which is valid over the entire region. In t his way, we avoid the divergent self-gravity at the position of the pa rticle and derive the equations of motion from the consistency conditi on of the matching. The matching is done to the order necessary to inc lude the effect of radiation reaction of O(Gm) with respect to the bac kground metric as well as the effect of spin-induced force. The reacti on term of O(Gm) is found to be completely due to tails of radiation, that is, due to curvature scattering of gravitational waves. In other words, the reaction force is found to depend on the entire history of the particle trajectory. Defining a regularized metric which consists of the background metric plus the tail part of the perturbed metric, w e find the equations of motion reduce to the geodesic equation on this regularized metric, except for the spin-induced force which is locall y expressed in terms of the curvature and spin tensors. Some implicati ons of the result and future issues are briefly discussed.