Prog. Theor. Phys. Vol. 90 No. 3 (1993) pp. 595-614

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

— Effect of Orbital Precession —

Masaru Shibata

Department of Physics, Kyoto University, Kyoto 606-01

(Received May 11, 1993)

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 θ_i for cos θ_i \gtrsim0.8, where θ_i 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.

URL : http://ptp.ipap.jp/link?PTP/90/595/
DOI : 10.1143/PTP.90.595

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