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We examine numerically the process of gravitational wave recoil in the merger of two black holes in non-head-on collision, in the realm of Robinson-Trautman spacetimes. Characteristic initial data for the system already presents a common aparent horizon so that the dynamics covers the post-merger phase up to the final configuration of the remnant black hole. Our analysis is based on the Bondi-Sachs conservation laws for the energy-momentum of the system. We evaluate the Bondi-Sachs momentum flux carried out by gravitational waves, the associated impulses and the net kick velocity $V_{k}$ due to the total impulse imparted to the merged system by the gravitational waves emitted. Typically for a non-head-on collision the net momentum flux carried out by gravitational waves is nonzero for equal-mass colliding black holes, a consequence of asymmetries of the initial data for this case. The distribution of $V_{k}$ as a function of the symmetric mass parameter $\eta$ is well fitted by a modified Fitchett $\eta$-scaling law and we give numerical evidence that the additional parameter modifying the law is a measure of the integrated gravitational wave momentum flux for the equal-mass case. For an initial infalling velocity $v/c \simeq 0.462$ of the colliding black holes and angle of collision $\rho_0=21^{\circ}$, we obtain a maximum $V_{k} \sim 121~{\rm km/s}$ located at $\eta \simeq 0.226$. For the equal-mass case we obtain $V_{k} \sim 107~{\rm km/s}$. Results for the net kick velocity in the head-on case are compared with numerical relativity calculations, and for a wide range of mass ratios ($0.3 \leq \alpha \leq 0.95$) we have an agreement to $5\%-8\%$ for PN+CLA and to $8\%-18\%$ for full numerical relativity, suggesting a close relation between the head-on initial data and its dynamics and the merger of binary systems.

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