Classical and Quantum Two-Body Problem in General Relativity

Abstract

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.

The republication of this 35-year-old paper in the electronic archive has been stimulated by the increased interest in binary (coalescing) black holes as a source of gravitational waves and by its close relation to the now popular "effective one body approach" to the general relativistic two-body problem, v.2 typos corrected