  The post-Newtonian approximation is a method for solving Einstein's field
equations for physical systems in which motions are slow compared to the speed
of light and where gravitational fields are weak. Yet it has proven to be
remarkably effective in describing certain strong-field, fast-motion systems,
including binary pulsars containing dense neutron stars and binary black hole
systems inspiraling toward a final merger. The reasons for this effectiveness
are largely unknown. When carried to high orders in the post-Newtonian
sequence, predictions for the gravitational-wave signal from inspiraling
compact binaries will play a key role in gravitational-wave detection by
laser-interferometric observatories.
