Gravitational radiation from a particle in circular orbit around a black hole. VI. Accuracy of the post-Newtonian expansion

TL;DR

This paper evaluates the accuracy of the post-Newtonian expansion in modeling gravitational waves emitted by a particle in circular orbit around a black hole, comparing it to exact numerical solutions to assess its effectiveness.

Contribution

It provides a quantitative assessment of the post-Newtonian expansion's accuracy for gravitational wave predictions in black hole binary systems.

Findings

Post-Newtonian expansion closely approximates exact solutions for slow-moving particles.

The reduction in signal-to-noise ratio due to nonoptimal filtering is quantified.

Results inform the reliability of analytical waveforms in gravitational wave detection.

Abstract

A particle of mass $\mu$ moves on a circular orbit around a nonrotating black hole of mass $M$. Under the assumption $\mu \ll M$ the gravitational waves emitted by such a binary system can be calculated exactly numerically using black-hole perturbation theory. If, further, the particle is slowly moving, then the waves can be calculated approximately analytically, and expressed in the form of a post-Newtonian expansion. We determine the accuracy of this expansion in a quantitative way by calculating the reduction in signal-to-noise ratio incurred when matched filtering the exact signal with a nonoptimal, post-Newtonian filter.