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

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.

9 pages, latex, no figures. Minor amendments, comments, new references and acknowledgments added

References in corpus (5)

• Effective one-body approach to general relativistic two-body dynamics
• On the determination of the last stable orbit for circular general relativistic binaries at the third post-Newtonian approximation
• Poincaré invariance in the ADM Hamiltonian approach to the general relativistic two-body problem
• Dynamical invariants for general relativistic two-body systems at the third post-Newtonian approximation
• Equivalence between the ADM-Hamiltonian and the harmonic-coordinates approaches to the third post-Newtonian dynamics of compact binaries

Cited by in corpus (7)

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• Magnetic States at Short Distances
• Binary black holes in Mkns as sources of gravitational radiation for space based interferometers
• Baryon Spectrum Analysis using Dirac's Covariant Constraint Dynamics
• Relative motion in spacetime