Gravitational wave recoils in non-axisymmetric Robinson-Trautman spacetimes

Abstract

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 ($3^{\circ }\le {\rho }_0\le 110^{\circ }$) 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 $190km/s$ for for the boost parameter considered. For ${\rho }_0\ge 50^{\circ }$ 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.

10 pages, 5 figures. arXiv admin note: substantial text overlap with arXiv:1403.4581, arXiv:1202.1271, arXiv:1111.1223

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