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

Edward K. Porter
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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.

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Edward K. Porter. 2006-09-05. The Cauchy convergence of T and P-approximant templates for test-mass Kerr binary systems. https://doi.org/10.1088/0264-9381%2F23%2F11%2F011

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