Gravitational Waves Induced by a Particle Orbiting around a Rotating Black Hole

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Abstract
We have calculated the energy and the angular momentum fluxes of gravitational waves induced by a test particle of mass µ, the orbital radius r0 and the Carter constant C moving around a Kerr black hole of mass M ≫µ and the angular momentum aM. In this case the orbital plane of the particle precesses around the symmetric axis due to the spin-orbit interaction. It is found that the energy flux is approximately written as a linear function of cos θi for cos θi \gtrsim0.8, where θi is the inclination of the orbital plane to the equatorial plane. It is also found that the orbital precession drastically modifies the wave pattern of gravitational waves. We propose a method to calculate the back reaction to the Carter constant and show a table of the fluxes of the Carter constant as well as the energy, angular momentum for various combinations of a, r0 and C. Using those fluxes, we perform a rough estimation of the time evolution of the inclination angle. It seems that the inclination angle of the orbital plane gradually becomes small for a ≪ 0 case and becomes large for a > 0 case due to the back reaction of the gravitational radiation.

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