Effective one-body approach to general relativistic two-body dynamics

TL;DR

This paper introduces an effective one-body framework that models the complex relativistic two-body problem as a test particle in an external metric, enabling non-perturbative analysis of binary coalescence dynamics.

Contribution

It presents a novel non-perturbative method to map the two-body problem onto an effective one-body problem, predicting the transition from inspiral to plunge in binary systems.

Findings

Predicts the transition from inspiral to plunge occurs before the innermost stable circular orbit.

Determines the binding energy, angular momentum, and orbital frequency at the innermost stable orbit.

Provides a framework for analyzing late-stage binary coalescence in general relativity.

Abstract

We map the general relativistic two-body problem onto that of a test particle moving in an effective external metric. This effective-one-body approach defines, in a non-perturbative manner, the late dynamical evolution of a coalescing binary system of compact objects. The transition from the adiabatic inspiral, driven by gravitational radiation damping, to an unstable plunge, induced by strong spacetime curvature, is predicted to occur for orbits more tightly bound than the innermost stable circular orbit in a Schwarzschild metric of mass M = m1 + m2. The binding energy, angular momentum and orbital frequency of the innermost stable circular orbit for the time-symmetric two-body problem are determined as a function of the mass ratio.