Gravitational waves induced by a spinning particle falling into a rotating black hole.

Abstract

Using the formalisms of Teukolsky and of Sasaki and Nakamura for the perturbation around a Kerr black hole we calculate the energy flux and the waveform of gravitational waves induced by a spinning particle of mass \ensuremath{\mu} and spin S falling from infinity with zero in-fall velocity into a rotating black hole of mass M\ensuremath{\gg}\ensuremath{\mu} and spin a along 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 derived by Dixon. Thus, there appear two additional effects due to the spin of the particle: one is due to the spin-spin interaction force which appears in the equations of motion and the other is due to the contribution of the energy-momentum tensor of the spinning particle. From numerical calculations, it is found that these spin effects are very important: In the case of a=S=0.99M, the total energy flux becomes 0.0106(\ensuremath{\mu}/M${)}^{2}$M, which is almost the same as that obtained by Davis et al. for a=S=0, while in the case of a=-S=0.99M, it becomes 0.0298(\ensuremath{\mu}/M${)}^{2}$M, i.e., about three times larger. We also show that the contribution of the energy-momentum tensor of the spinning particle dominates over that of the spin-spin interaction term in the equations of motion. The results obtained in this paper will be an important guideline to quantitative estimates of gravitational waves in numerical relativistic simulations of the head-on collision of two spinning black holes. \textcopyright{} 1996 The American Physical Society.