Gravitational Wave Induced by a Particle Orbiting around a Schwarzschild Black Hole

We have calculated gravitational waves induced by a test particle with eccentric orbits around a Schwarzschild black hole. The energy and angular momentum fluxes of gravitational waves emitted from various types of the orbits are shown. Comparing our results with those calculated by the semi-relativistic quadrupole formula, we find that, even for orbits with r~30 M, the amount and wave form of gravitational radiation are predominantly determined by the relativistic property, such as higher multipole contribution and curvature scattering effect of gravitational waves. We find that even in the case of circular orbits the wave form is highly deformed from a sine curve, indicating the importance of higher multipole contributions. On the other hand, the total energy flux emitted by gravitational waves is well estimated by the semi-relativistic quadrupole formula accidentally. Implications of these results to future detection of gravitational waves from a coalescing binary are also discussed.