  We investigate the asymptotic behavior of peculiar velocities in certain
physically significant time-dependent gravitational fields. Previous studies of
the motion of free test particles have focused on the \emph{collapse scenario},
according to which a double-jet pattern with Lorentz factor $\gamma \to \infty$
develops asymptotically along the direction of complete gravitational collapse.
In the present work, we identify a second \emph{wave scenario}, in which a
single-jet pattern with Lorentz factor $\gamma \to \infty$ develops
asymptotically along the direction of wave propagation. The possibility of a
connection between the two scenarios for the formation of cosmic jets is
critically examined.
