General Relativistic Dynamics of Compact Binary Systems

TL;DR

This paper derives the equations of motion for compact binary systems in general relativity up to 3.5PN order, analyzing their stability and finding no innermost stable circular orbit at this level for equal masses.

Contribution

It provides a 3.5PN order derivation of the equations of motion and investigates the stability of circular orbits, revealing no ISCO at 3PN for equal-mass binaries.

Findings

No innermost stable circular orbit (ISCO) at 3PN order for equal masses.

Equations of motion derived from a generalized Lagrangian and Hamiltonian form.

Stability analysis of circular orbits up to 3PN order.

Abstract

The equations of motion of compact binary systems have been derived in the post-Newtonian (PN) approximation of general relativity. The current level of accuracy is 3.5PN order. The conservative part of the equations of motion (neglecting the radiation reaction damping terms) is deducible from a generalized Lagrangian in harmonic coordinates, or equivalently from an ordinary Hamiltonian in ADM coordinates. As an application we investigate the problem of the dynamical stability of circular binary orbits against gravitational perturbations up to the 3PN order. We find that there is no innermost stable circular orbit or ISCO at the 3PN order for equal masses.