The observation of gravitational-radiation damping in the binary pulsar PSR 1913 + 16 and the ongoing experimental search for gravitational waves of extraterrestrial origin have made the theory of gravitational radiation an active branch of classical general relativity. In calculations of gravitational radiation, approximation methods play a crucial role. We summarize recent developments in two areas in which approximations are important: (a) the quadrupole approximation, which determines the energy flux and the radiation reaction forces in weak-field, slow-motion, source-within-the-near-zone systems such as the binary pulsar; and (b) the normal modes of oscillation of black holes, where the Wentzel–Kramers–Brillouin approximation gives accurate estimates of the complex frequencies of the modes.
Gravitational radiation reaction in compact binary systems: Contribution of the quadrupole-monopole interaction