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.
Keywords
Cite
@article{arxiv.1611.02943,
title = {Classical and Quantum Two-Body Problem in General Relativity},
author = {Amar Maheshwari and Emil Nissimov and Ivan Todorov},
journal= {arXiv preprint arXiv:1611.02943},
year = {2019}
}
Comments
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