Gravitational wave momentum extraction in non-axisymmetric Robinson-Trautman spacetimes (1403.4581v1)

Abstract: 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.