Gravitational wave recoils in non-axisymmetric Robinson-Trautman spacetimes

We examine the gravitational wave recoil waves and the associated net kick velocities in non-axisymmetric Robinson-Trautman spacetimes. We use characteristic initial data for the dynamics corresponding to non-head-on collisions of black holes. We make a parameter study of the kick distributions, corresponding to an extended range of the incidence angle $\rho_0$ in the initial data. For the range of $\rho_0$ examined ($3^{\circ} \leq \rho_0 \leq 110^{\circ}$) the kick distributions as a function of the symmetric mass parameter $\eta$ satisfy a law obtained from an empirical modification of the Fitchett law, with a parameter $C$ that accounts for the non-zero net gravitational momentum wave fluxes for the equal mass case. The law fits accurately the kick distributions for the range of $\rho_0$ examined, with a rms normalized error of the order of $5 \%$. For the equal mass case the nonzero net gravitational wave momentum flux increases as $\rho_0$ increases, up to $\rho_0 \simeq 55^{\circ}$ beyond which it decreases. The maximum net kick velocity is about $190 {\rm km/s}$ for for the boost parameter considered. For $\rho_0 \geq 50^{\circ}$ the distribution is a monotonous function of $\eta$. The angular patterns of the gravitational waves emitted are examined. Our analysis includes the two polarization modes present in wave zone curvature.