The radiation reaction force and balance equations are derived for slow-motion, gravitationally bound systems with compact components such as neutron stars and black holes. To obtain these results, use is made of the Einstein-Infeld-Hoffmann (EIH) procedure. As a consequence, all quantities involved in the derivation are finite and hence no renormalization is required. Furthermore, no laws of motion for the components need be assumed. Approximate expressions for the fields required to evaluate the EIH surface integrals are obtained using the methods of matched asymptotic expansions and multiple time scales. The results obtained are the same as those derived previously for systems with noncompact components.

• Received 3 December 1986

DOI:https://doi.org/10.1103/PhysRevD.36.2301