Classical and Quantum Two-Body Problem in General Relativity

TL;DR

This paper models the two-body problem in general relativity by reducing it to an effective particle in an external field, deriving an effective potential from linearized quantum gravity, relevant for relativistic velocities.

Contribution

It introduces a novel approach to the two-body problem using an effective particle and quantum gravity techniques, providing a Schwarzschild-like potential with two radii.

Findings

Effective potential derived from Born diagram in linearized quantum gravity.

Potential reduces to Schwarzschild-like form with two radii.

Results applicable to relativistic velocities in weak fields.

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.