Gravitational waves from a particle orbiting around a rotating black hole: Post-Newtonian expansion

Using the Teukolsky and Sasaki-Nakamura equations for the gravitational perturbation of 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 ${\mathrm{post}}^{5/2}$-Newtonian (${\mathrm{P}}^{5/2}$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 ${\mathrm{P}}^{3/2}$N order is in agreement with a similar calculation by Poisson as well as with the standard post-Newtonian calculation by Kidder, Will, and Wiseman. 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 ${\mathrm{P}}^2$N and ${\mathrm{P}}^{5/2}$N corrections are important to construct effective template waveforms which will be used for future laser-interferometric gravitational wave detectors.