radius, and therefore no problem in the evaluation of physical quantities is present. This might be at first surprising, but in reality the Zerilli function deos noe play any physical role, it is its time derivative what does, and the latter does not have any unusual asymptotic behavior. To put it in different terms: one could carry out perturbation theory and work out all relevant physics entirely in terms of the time derivative of the Zerilli function (which also satisfies the Zerilli equation) and there one would not see any unusual asymptotic behavior.

Another aspect that could cause concern is the nature of the gauge transformation considered. The gauge transformation is well behaved in any finite value of $r_*$ (that is, any point of the exterior of the black hole excluding the horizon and spatial infinity). Since in order to compute the radiated energies and waveforms we will never need information from either the horizon nor infinity, the gauge transformation is well defined in all relevant points for our calculation.

Results and conclusions
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We have numerically evolved the Zerilli equation with the initial data presented above and computed the energy and waveforms for the “relaxation” of a single boosted 