Post-Newtonian expansion of gravitational waves from a particle in circular orbits around a rotating black hole: Up to $O(v^8)$ beyond the quadrupole formula

TL;DR

This paper extends the post-Newtonian expansion of gravitational wave luminosities for a particle orbiting a rotating black hole up to order v^8, highlighting the importance of spin effects at higher orders for accurate waveform modeling.

Contribution

It provides the first calculation of gravitational wave luminosities including spin-dependent terms up to O(v^8), improving the understanding of waveforms from coalescing binaries.

Findings

Spin-dependent terms appear at each post-Newtonian order.

At O(v^6), spin effects significantly influence orbital phase evolution.

Including O(v^6) and O(v^7) terms improves accuracy; O(v^8) does not.

Abstract

Extending a method developed by Sasaki in the Schwarzschild case and by Shibata, Sasaki, Tagoshi, and Tanaka in the Kerr case, we calculate the post-Newtonian expansion of the gravitational wave luminosities from a test particle in circular orbit around a rotating black hole up to $O(v^8)$ beyond the quadrupole formula. The orbit of a test particle is restricted on the equatorial plane. We find that spin dependent terms appear in each post-Newtonian order, and that at $O(v^6)$ they have a significant effect on the orbital phase evolution of coalescing compact binaries. By comparing the post-Newtonian formula of the luminosity with numerical results we find that, for $30M\lesssim r \lesssim 100M$, the spin dependent terms at $O(v^6)$ and $O(v^7)$ improve the accuracy of the post-Newtonian formula significantly, but those at $O(v^8)$ do not improve.