Gravitational waveforms from a point particle orbiting a Schwarzschild black hole

Abstract

We numerically solve the inhomogeneous Zerilli-Moncrief and Regge-Wheeler equations in the time domain. We obtain the gravitational waveforms produced by a point particle of mass $\ensuremath{\mu}$ traveling around a Schwarzschild black hole of mass M on arbitrary bound and unbound orbits. Fluxes of energy and angular momentum at infinity and the event horizon are also calculated. Results for circular orbits, selected cases of eccentric orbits, and parabolic orbits are presented. The numerical results from the time-domain code indicate that, for all three types of orbital motion, black hole absorption contributes less than 1% of the total flux, so long as the orbital radius ${r}_{p}(t)$ satisfies ${r}_{p}(t)>5M$ at all times.