Post-Newtonian Expansion of Gravitational Radiation

TL;DR

This paper reviews the post-Newtonian expansion method for modeling gravitational waveforms from inspiralling compact binaries, focusing on multipole moments and the treatment of point-particles in high-order approximations.

Contribution

It provides a detailed summary of the multipole expansion formalism and discusses the regularization of point-particles in high post-Newtonian orders.

Findings

Formalism applicable to point-particles with regularization

Matching exterior and interior fields via multipole moments

Insights into high-order post-Newtonian approximations

Abstract

The post-Newtonian expansion appears to be a relevant tool for predicting the gravitational waveforms generated by some astrophysical systems such as binaries. In particular, inspiralling compact binaries are well-modelled by a system of two point-particles moving on a quasi-circular orbit whose decay by emission of gravitational radiation is described by a post-Newtonian expansion. In this paper we summarize the basics of the computation by means of a series of multipole moments of the exterior field generated by an isolated source in the post-Newtonian approximation. This computation relies on an ansatz of matching the exterior multipolar field to the inner field of a slowly-moving source. The formalism can be applied to point-particles at the price of a further ansatz, that the infinite self-field of point-particles can be regularized in a certain way. As it turns out, the concept of point-particle requires a precise definition in high post-Newtonian approximations of general relativity.