Post-Newtonian Expansion of Gravitational Waves from a Particle in Circular Orbits around a Rotating Black Hole: Effects of Black Hole Absorption

When a particle moves around a Kerr black hole, it radiates gravitational waves. Some of these waves are absorbed by the black hole. We calculate such absorption of gravitational waves induced by a particle of mass mu in a circular orbit on an equatorial plane around a Kerr black hole of mass M. We assume that the velocity of the particle v is much smaller than the speed of light c and calculate the energy absorption rate analytically. We adopt an analytic technique for the Teukolsky equation developed by Mano, Suzuki and Takasugi. We obtain the energy absorption rate to O ( (v/c) ⁸) compared to the lowest order. We find that the black hole absorption occurs at O ( (v/c) ⁵) beyond the Newtonian-quadrapole luminosity at infinity in the case when the black hole is rotating, which is O ( (v/c) ³) lower than the non-rotating case. Using the energy absorption rate, we investigate its effects on the orbital evolution of coalescing compact binaries.