  We show how the concurrent implementation of the exact solutions of the
Einstein equations, of the equations of motion of the test particles, and of
the relativistic estimate of the emission of gravitational waves from test
particles, can establish a priori constraints on the possible phenomena
occurring in Nature. Two examples of test particles starting at infinite
distance or from finite distance in a circular orbit around a Kerr black hole
are considered: the first leads to a well defined gravitational wave burst the
second to a smooth merging into the black hole. This analysis is necessary for
the study of the waveforms in merging binary systems.
