Classical and quantum two-body problem in general relativity

The two-body problem in general relativity is reduced to the problem of an effective particle (with an energy-dependent relativistic reduced mass) in an external field. The effective potential is evaluated from the Born diagram of the linearized quantum theory of gravity. It reduces to a Schwarzschild-like potential with two different Schwarzschild radii. The results derived in a weak field approximation are expected to be relevant for relativistic velocities.Revised version of Trieste preprint IC/80/124 (August 1980).A similar approach is being developed by a number of authors (see, e.g., References [9] and [10]); the reader will find a comprehensive bibliography in References [11] and [8].