Two-body problem in general relativity

Remarks

Unlike the Newtonian two-body problem, it has no exact solution in closed form, and the motion cannot be reduced to that of one body in a fixed field. The orbits do not close, because of periastron precession, and they shrink because of gravitational radiation reaction. Einstein, Infeld and Hoffmann gave in 1938 the first post-Newtonian equations of motion for several bodies derived from the field equations. The post-Newtonian expansion describes the slow inspiral, and has been carried to high orders. Perturbation theory around a black hole, through the gravitational self-force, describes binaries with very unequal masses. Numerical relativity solves the full equations near merger; the first complete simulations of the inspiral and merger of two black holes were achieved by Pretorius in 2005. Effective one-body models combine these approaches into waveform templates. Such templates were used to identify the first directly detected gravitational wave signal, from a binary black hole merger, observed in 2015.