On the Unreasonable Effectiveness of post-Newtonian Theory in Gravitational-Wave Physics

The first indirect detection of gravitational waves involved a binary system of neutron stars. In the future, the first direct detection may also involve binary systems -- inspiralling and merging binary neutron stars or black holes. This means that it is essential to understand in full detail the two-body system in general relativity, a notoriously difficult problem with a long history. Post-Newtonian approximation methods are thought to work only under slow motion and weak field conditions, while numerical solutions of Einstein's equations are thought to be limited to the final merger phase. Recent results have shown that post-Newtonian approximations seem to remain unreasonably valid well into the relativistic regime, while advances in numerical relativity now permit solutions for numerous orbits before merger. It is now possible to envision linking post-Newtonian theory and numerical relativity to obtain a complete "solution" of the general relativistic two-body problem. These solutions will play a central role in detecting and understanding gravitational wave signals received by interferometric observatories on Earth and in space.