Gravitational wave recoil in Robinson-Trautman spacetimes

We consider the gravitational recoil due to non-reflection-symmetric gravitational wave emission in the context of axisymmetric Robinson-Trautman spacetimes. We show that regular initial data evolve generically into a final configuration corresponding to a Schwarzschild black-hole moving with constant speed. For the case of (reflection-)symmetric initial configurations, the mass of the remnant black-hole and the total energy radiated away are completely determined by the initial data, allowing us to obtain analytical expressions for some recent numerical results that have been appeared in the literature. Moreover, by using the Galerkin spectral method to analyze the non-linear regime of the Robinson-Trautman equations, we show that the recoil velocity can be estimated with good accuracy from some asymmetry measures (namely the first odd moments) of the initial data. The extension for the non-axisymmetric case and the implications of our results for realistic situations involving head-on collision of two black holes are also discussed.