GRAVITATIONAL-WAVES INDUCED BY A SPINNING PARTICLE FALLING INTO A ROTATING BLACK-HOLE

Using the formalisms of Teukolsky and of Sasaki and Nakamura for the p erturbation around a Kerr black hole we calculate the energy flux and the waveform of gravitational waves induced by a spinning particle of mass mu and spin S falling from infinity with zero in-fall velocity in to a rotating black hole of mass M much greater than mu and spin a alo ng the z axis. The calculations are performed combining the Teukolsky formalism with the equations of motion of a spinning particle derived by Papapetrou and the energy-momentum tensor of a spinning particle de rived by Dixon. Thus, there appear two additional effects due to the s pin of the particle: one is due to the spin-spin interaction force whi ch appears in the equations of motion and the other is due to the cont ribution of the energy-momentum tensor of the-spinning particle. From numerical calculations, it is found that these spin effects are very i mportant: In the case of a = S = 0.99M, the total energy flux becomes 0.0106(mu/M)(2)M, which is almost the same as that obtained by Davis e t al, for a S = 0, while in the case of a = -S = 0.99M, it becomes 0.0 298(mu/M)(2)M, i.e., about three times larger. We also show that the c ontribution of the energy-momentum tensor of the spinning particle dom inates over that of the spin-spin interaction term in the equations of motion. The results obtained in this paper will be an important guide line to quantitative estimates of gravitational waves in numerical rel ativistic simulations of the head-on collision of two spinning black h oles.