The Cauchy convergence of T and P-approximant templates for test-mass Kerr binary systems

TL;DR

This paper investigates the convergence properties of T- and P-approximant gravitational wave templates for test-mass Kerr binary systems, demonstrating that P-approximants converge faster and are more effective for detection.

Contribution

It provides a detailed analysis of the Cauchy convergence of P-approximant templates, establishing their superiority over standard post-Newtonian templates for Kerr systems.

Findings

P-approximant templates show faster Cauchy convergence.

P-approximants yield higher fitting factors.

P-approximants are more effective for parameter estimation.

Abstract

In this work we examine the Cauchy convergence of both post-Newtonian (T-approximant) and re-summed post-Newtonian (P-approximant) templates for the case of a test-mass orbiting a Kerr black hole along a circular equatorial orbit. The Cauchy criterion demands that the inner product between the $n$ and $n+1$ order approximation approaches unity, as we increase the order of approximation. In previous works, it has been shown that we achieve greater fitting factors and better parameter estimation using the P-approximant templates for both Schwarzschild and Kerr black holes. In this work, we show that the P-approximant templates also display a faster Cauchy convergence making them a superior template to the standard post-Newtonian templates.