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

Abstract

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. § 1. Introduction 65 Coalescence of two compact objects, such as neutron star-neutron star, neutron star-black hole and/or black hole-black hole binaries, is one of the promising sources of gravitational radiation which may be detected by future laser interferometric detectors, LIGOl) and VIRGO. 2) Such binaries are thought to evolve in the following sequence: At first two compact objects move around each other with an eccentric orbit. As gravitational waves are emitted, both the orbital radius and the eccentricity gradually decrease. If the orbit becomes circular before the radius becomes too small, regular monochromatic gravitational waves are emitted for a sufficiently long time interval. Depending on the mass of each compact object, various phenomena will occur. For example, for almost equal mass neutron star case, when the separation of two stars becomes smaller than the radius of the last stable circular orbit, r ~6Mtot, where Mtot is the total,mass of the system, or a certain critical radius below which gravitational-radiation damping is severe, they plunge into each other and merge. Then the merging object will be a rotating black hole. To investigate gravitational waves radiated in the above evolutionary sequence in detail, great efforts have been made by many researchers recently. As for the final coalescence phase, Nakamura, Oohara and Shibata 3)-5) performed 3D post-Newtonian hydrodynamic simulations of coalescence of neutron stars with a wide range of initial conditions. They showed how the gravitational wave emission depends on the post-Newtonian effect, the spin of each neutron star and the plunging velocity. However their simulations should be considered as a first step to the study of real