Gravitational Radiation from a Particle with Orbital Angular Momentum Plunging into a Kerr Black Hole

Using the Sasaki-Nakamura equation, we have computed the energy, linear and angular momentum of the gravitational radiation induced by a particle of mass µ and angular momentum µLz plunging in an equatorial plane into a Kerr black hole of mass M (≫µ) and angular momentum Ma. It is found that the total energy ΔE ≈(µ/ M) µc2 is emitted by the particle with sufficient large orbital angular momentum. For the same value of |Lz|, a corotating particle emits more energy than a counter-rotating one. We have also calculated the energy from a rotating ring plunging into a Kerr black hole. In this case, we have found that a corotating ring emits less gravitational energy than a counter-rotating one for the same |Lz|. The maximum of the linear momentum is 6 ×10-2(µ/ M) µc, which suggests the recoil velocity of the coalesced black hole is 160 km/s for µ= 0.1 M.