  We examine numerically the gravitational wave recoil in non-axisymmetric
Robinson-Trautman spacetimes. We construct characteristic initial data for the
Robinson-Trautman dynamics which are interpreted as corresponding to the early
post-merger state of two boosted colliding black holes with a common apparent
horizon. Our analysis is based on the Bondi-Sachs energy-momentum conservation
laws which regulate the radiative transfer processes involved in the emission
of gravitational waves. We evaluate the Bondi-Sachs momentum flux carried out
by gravitational waves and the associated net kick velocity defined (in a
zero-initial-Bondi-momentum frame) as proportional to the total gravitational
wave impulse imparted on the system. The kick velocity distributions are
obtained and analyzed for two distinct classes of initial data corresponding to
the early post-merger state of (i) non-head-on collisions and (ii) head-on
collisions of black holes. For the first class (i), the net gravitational wave
momentum fluxes and associated kicks are evaluated for a given domain of
parameters (incidence angle and mass ratio). Typically for the equal mass case
the net gravitational wave momentum flux carried is nonzero. This last result
indicates that these configurations are not connected with black hole binary
inspirals or head-on collisions. We suggest that these systems might be a
candidate to an approximate description of the post-merger phase of a
non-head-on collision of black holes not preceded by a pre-merger inspiral
phase, as for instance colliding black holes in pre-merger unbounded
trajectories. For the second class (ii), head-on collisions, we compare our
results, and discuss the analogies, with $1+3$ numerical relativity simulations
of binary black hole inspirals and head-on collisions.
