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.