Note on Accuracy of the Post-Newtonian Approximation for Extreme-Mass Ratio Inspirals: Retrograde Orbits

TL;DR

This paper investigates the accuracy limits of the post-Newtonian approximation for retrograde orbits in extreme-mass ratio inspirals, revealing complex behaviors near the approximation's validity boundary.

Contribution

It provides a detailed analysis of the validity region of the post-Newtonian approximation for retrograde orbits using numerical and analytical flux calculations.

Findings

The validity region boundary exhibits intricate behavior.

Higher post-Newtonian orders do not necessarily extend the approximation's validity.

Retrograde orbits show unique features in the approximation's applicability.

Abstract

The post-Newtonian approximation is useful to discuss gravitational waveforms for binary inspirals. In this note, for retrograde circular orbits in the equatorial plane, we discuss the region of validity of the post-Newtonian approximation by using the gravitational energy flux derived numerically and analytically in the black hole perturbation approach. It is found that the edge of the allowable region behaves quite intricately, including prograde orbits even if we treat higher post-Newtonian orders.