Post-Newtonian theory and the two-body problem

TL;DR

This article presents a comprehensive framework for the post-Newtonian (PN) treatment of the two-body problem in general relativity, spanning from the fundamental field equations in harmonic coordinates to the generation of gravitational-wave templates for inspiralling binaries. It elucidates the near-zone PN expansion, the matching to an exterior multipolar field, and the role of multipole source moments and radiative moments, including hereditary tail effects, in shaping waveforms. Regularization techniques—Hadamard and dimensional regularization—are developed to handle point-particle singularities and remove 3PN ambiguities, enabling unambiguous predictions for binary dynamics and radiation up to $3.5$PN. The work culminates in detailed results for spinning bodies, energy and flux expressions, and explicit waveform modes (notably $h^{22}$) that underpin accurate templates for gravitational-wave detection and parameter estimation in current and future detectors.

Abstract

Reliable predictions of general relativity theory are extracted using approximation methods. Among these, the powerful post-Newtonian approximation provides us with our best insights into the problems of motion and gravitational radiation of systems of compact objects. This approximation has reached an impressive mature status, because of important progress regarding its theoretical foundations, and the successful construction of templates of gravitational waves emitted by inspiralling compact binaries. The post-Newtonian predictions are routinely used for searching and analyzing the very weak signals of gravitational waves in current generations of detectors. High-accuracy comparisons with the results of numerical simulations for the merger and ring-down of binary black holes are going on. In this article we give an overview on the general formulation of the post-Newtonian approximation and present up-to-date results for the templates of compact binary inspiral.