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

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 ${\mathrm{P}}^{5/2}\mathrm{N}$ 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.

phyzzx 41 pages

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• The Last Three Minutes: Issues in Gravitational Wave Measurements of Coalescing Compact Binaries
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