Effective one-body approach to the relativistic two-body problem

TL;DR

This paper extends the effective one-body approach to the relativistic two-body problem, demonstrating its applicability to classical electromagnetic and gravitational interactions, with implications for binary pulsar studies and tests of general relativity.

Contribution

It shows that the relativistic reduced mass and effective particle energy concept effectively describe the classical relativistic two-body problem, including gravitational interactions.

Findings

Applicable to electromagnetic and gravitational interactions

Provides a framework for analyzing binary pulsars

Compared with recent alternative methods

Abstract

The relativistic 2-body problem, much like the non-relativistic one, is reduced to describing the motion of an effective particle in an external field. The concept of a relativistic reduced mass and effective particle energy introduced some 30 years ago to compute relativistic corrections to the Balmer formula in quantum electrodynamics, is shown to work equally well for classical electromagnetic and gravitational interaction. The results for the gravitational 2-body problem have more than academic interest since they apply to the study of binary pulsars that provide precision tests for general relativity. They are compared with recent results derived by other methods.