On the two-body problem in general relativity

TL;DR

This paper discusses the equations of motion for compact binary systems in general relativity at the third post-Newtonian order, crucial for gravitational wave detection.

Contribution

It provides recent results on the equations of motion and Lagrangian formulation at the third post-Newtonian order for compact binaries.

Findings

Derived equations of motion at 3PN order

Formulated the Lagrangian for binary systems at this order

Facilitates the creation of gravitational wave templates

Abstract

We consider the two-body problem in post-Newtonian approximations of general relativity. We report the recent results concerning the equations of motion, and the associated Lagrangian formulation, of compact binary systems, at the third post-Newtonian order (1/c^6 beyond the Newtonian acceleration). These equations are necessary when constructing the theoretical templates for searching and analyzing the gravitational-wave signals from inspiralling compact binaries in VIRGO-type experiments.