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A one-parameter family of time-symmetric initial data for the radial infallof a particle into a Schwarzschild black hole is constructed within theframework of black-hole perturbation theory. The parameter measures the amountof gravitational radiation present on the initial spacelike surface. Theseinitial data sets are then evolved by integrating the Zerilli-Moncrief waveequation in the presence of the particle. Numerical results for thegravitational waveforms and their power spectra are presented; we show that thechoice of initial data strongly influences the waveforms, both in their shapesand their frequency content. We also calculate the total energy radiated by theparticle-black-hole system, as a function of the initial separation between theparticle and the black hole, and as a function of the choice of initial data.Our results confirm that for large initial separations, a conformally-flatinitial three-geometry minimizes the initial gravitational-wave content, sothat the total energy radiated is also minimized. For small initialseparations, however, we show that the conformally-flat solution no longerminimizes the energy radiated.Comment: ReVTeX, 34 pages, 13 figures, 1 table, appendix containting a  convergence test of our code is now include

One-parameter family of time-symmetric initial data for the radial infall of a particle into a Schwarzschild black hole