Gravitational waveforms from a point particle orbiting a Schwarzschild black hole

TL;DR

This paper presents a numerical time-domain method to compute gravitational waveforms and fluxes from a point particle orbiting a Schwarzschild black hole, covering various orbital configurations and analyzing black hole absorption effects.

Contribution

It introduces a time-domain numerical approach to calculate gravitational waveforms and fluxes for arbitrary bound and unbound orbits around a Schwarzschild black hole, including absorption effects.

Findings

Black hole absorption contributes less than 1% of total flux for r_p(t)> 5M.

The method accurately models circular, eccentric, and parabolic orbits.

Flux calculations include energy and angular momentum at infinity and the horizon.

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 $\mu$ 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.