Accuracy of the Post-Newtonian Approximation for Extreme-Mass Ratio Inspirals from Black-hole Perturbation Approach

TL;DR

This paper assesses the accuracy and validity regions of the post-Newtonian approximation for extreme-mass ratio inspirals in Kerr spacetime, using analytical and numerical methods, and finds higher PN orders extend validity.

Contribution

It provides a detailed analysis of the validity regions of the post-Newtonian approximation for black hole perturbations, highlighting the benefits of higher PN orders.

Findings

Higher PN orders increase the regions of validity.

Local maxima in validity regions occur at lower PN orders.

Encourages higher PN order calculations for comparable-mass binaries.

Abstract

We revisit the accuracy of the post-Newtonian (PN) approximation and its region of validity for quasi-circular orbits of a point particle in the Kerr spacetime, by using an analytically known highest post-Newtonian order gravitational energy flux and accurate numerical results in the black hole perturbation approach. It is found that regions of validity become larger for higher PN order results although there are several local maximums in regions of validity for relatively low-PN order results. This might imply that higher PN order calculations are also encouraged for comparable-mass binaries.