  Black hole perturbation theory, or more generally, perturbation theory on a
Schwarzschild bockground, has been applied in several contexts, but usually
under the simplifying assumption that the ADM momentum vanishes, namely, that
the evolution is carried out and observed in the ``center of momentum frame''.
In this paper we consider some consequences of the inclusion of a non vanishing
ADM momentum in the initial data. We first provide a justification for the
validity of the transformation of the initial data to the ``center of momentum
frame'', and then analyze the effect of this transformation on the
gravitational wave amplitude. The most significant result is the possibility of
a type of gravitational memory effect that appears to have no simple relation
with the well known Christodoulou effect.
