Can the post-Newtonian gravitational waveform of an inspiraling binary be improved by solving the energy balance equation numerically?

TL;DR

This paper investigates whether numerically solving the post-Newtonian energy balance equation improves gravitational waveform templates for inspiraling binaries, finding no significant accuracy gain in the small mass ratio limit.

Contribution

It provides an analysis comparing numerical and analytical solutions of the energy balance equation for gravitational wave templates, focusing on the small mass ratio scenario.

Findings

Numerical solutions do not improve template accuracy in the small mass ratio limit.

Analytical post-Newtonian expansions remain sufficient for accurate waveform modeling.

The study clarifies the limitations of numerical approaches in this context.

Abstract

The detection of gravitational waves from inspiraling compact binaries using matched filtering depends crucially on the availability of accurate template waveforms. We determine whether the accuracy of the templates' phasing can be improved by solving the post-Newtonian energy balance equation numerically, rather than (as is normally done) analytically within the post-Newtonian perturbative expansion. By specializing to the limit of a small mass ratio, we find evidence that there is no gain in accuracy.