Gravitational Waves from a Particle Orbiting a Black Hole

5 Gravitational Waves from a Particle Orbiting a Black Hole

Based on the ingoing wave functions discussed in Section 3 and 4, we can derive the gravitational wave energy and angular momentum flux emitted to infinity. The formula for the energy and the angular momentum luminosity to infinity are given by Equations (48 ) and (49 ). Since most of the calculations are very long, we show only the final results. In [71 ], some details of the calculations are summarized. We define the post-Newtonian expansion parameter by $x ≡ (M Ωφ )1∕3$ , where $M$ is the mass of the black hole and $Ω φ$ is the orbital angular frequency of the particle. Since the parameter $x$ is directly related to the observable frequency, this result can be compared with the results by another method easily.

5.1 Circular orbit around a Schwarzschild black hole
5.2 Circular orbit on the equatorial plane around a Kerr black hole
5.3 Waveforms in the case of circular orbit
5.4 Slightly eccentric orbit around a Schwarzschild black hole
5.5 Slightly eccentric orbit around a Kerr black hole
5.6 Circular orbit with a small inclination from the equatorial plane around a Kerr black hole
5.7 Absorption of gravitational waves by a black hole
5.8 Adiabatic evolution of Carter constant for orbit with small eccentricity and small inclination angle around a Kerr black hole
5.9 Adiabatic evolution of constants of motion for orbits with generic inclination angle and with small eccentricity around a Kerr black hole