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The computation of the gravitational radiation emitted by a particle fallinginto a Schwarzschild black hole is a classic problem studied already in the1970s. Here we present a detailed numerical analysis of the case of radialinfall starting at infinity with no initial velocity. We compute the radiatedwaveforms, spectra and energies for multipoles up to l = 6, improvingsignificantly on the numerical accuracy of existing results. This is done byintegrating the Zerilli equation in the frequency domain using the Green'sfunction method. The resulting wave exhibits a "ring-down" phase whose dominantcontribution is a superposition of the quasi-normal modes of the black hole.The numerical accuracy allows us to recover the frequencies of these modesthrough a fit of that part of the wave. Comparing with direct computations ofthe quasi-normal modes we reach a \sim 10^{-4} to \sim 10^{-2} accuracy for thefirst two overtones of each multipole. Our numerical accuracy also allows us todisplay the power-law tail that the wave develops after the ring-down has beenexponentially cut-off. The amplitude of this contribution is \sim 10^2 to \sim10^3 times smaller than the typical scale of the wave.

physical review. d. particles, fields, gravitation, and cosmology/physical review. d, particles, fields, gravitation, and cosmology

Gravitational radiation from radial infall of a particle into a  Schwarzschild black hole. A numerical study of the spectra, quasi-normal  modes and power-law tails