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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

Hideyuki Tagoshi·Masaru Shibata·Takahiro Tanaka·Misao Sasaki
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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.

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Hideyuki Tagoshi, Masaru Shibata, Takahiro Tanaka, Misao Sasaki. 1996-03-19. 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. https://doi.org/10.1103/physrevd.54.1439

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