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

The computation of the gravitational radiation emitted by a particle falling into a Schwarzschild black hole is a classic problem that was already studied in the 1970s. Here we present a detailed numerical analysis of the case of radial infall starting at infinity with no initial velocity. We compute the radiated waveforms, spectra, and energies for multipoles up to l = 6, improving significantly on the numerical accuracy of existing results. This is done by integrating the Zerilli equation in the frequency domain using the Green's function method. The resulting wave exhibits a ring-down phase whose dominant contribution is a superposition of the quasinormal modes of the black hole. The numerical accuracy allows us to recover the frequencies of these modes through a fit of that part of the wave. Comparing with direct computations of the quasinormal modes, we reach a similar to 10(-4) to similar to 10(-2) accuracy for the first two overtones of each multipole. Our numerical accuracy also allows us to display the power-law tail that the wave develops after the ring-down has been exponentially cut off. The amplitude of this contribution is similar to 10(2) to similar to 10(3) times smaller than the typical scale of the wave.