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

TL;DR

This paper derives high-order post-Newtonian expansions for gravitational wave energy and angular momentum fluxes from particles orbiting rotating black holes, aiding the development of accurate waveform templates for gravitational wave detection.

Contribution

It extends the post-Newtonian expansion to P^{5/2}N order for Kerr spacetime using Sasaki's method, including effects of orbital inclination and spin.

Findings

Results agree with previous calculations at P^{3/2}N order.

Spin-dependent terms are crucial for accurate waveform templates.

The method improves modeling of gravitational waves from compact binary inspirals.

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.