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Gravitational Waves from a Particle Orbiting Around a Rotating Black Holes: Post-Newtonian Expansion

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

Using the Teukolsky and Sasaki-Nakamura equations for the gravitational perturbation of the Kerr spacetime, we calculate the post-Newtonian expansion of the energy and angular momentum luminosities of gravitational waves from a test particle orbiting around a rotating black hole up through ${\rm P^{5/2}N}$ order beyond the quadrupole formula. We apply a method recently developed by Sasaki to the case of a rotating black hole. We take into account a small inclination of the orbital plane to the lowest order of the Carter constant. The result to $ P^{3/2}N}$ order is in agreement with a similar calculation by Poisson as well as with the standard post-Newtonian calculation by Kidder et al. Using our result, we calculate the integrated phase of gravitational waves from a neutron star-neutron star binary and a black hole-neutron star binary during their inspiral stage. We find that, in both cases, spin-dependent terms in the P$^2$N and P$^{5/2}$N corrections are important to construct effective template waveforms which will be used for future laser-interferometric gravitational wave detectors.

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Masaru Shibata, Misao Sasaki, Hideyuki Tagoshi, Takahiro Tanaka. 1994-09-27. Gravitational Waves from a Particle Orbiting Around a Rotating Black Holes: Post-Newtonian Expansion. https://doi.org/10.1103/physrevd.51.1646

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