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• W1990262032 abstract "We examine numerically the process of momentum extraction by gravitational waves in the merger of two colliding black holes, in the realm of Robinson-Trautman spacetimes. The initial data have already a common horizon so that the evolution covers the post-merger phase up to the final configuration of the remnant black hole. The analysis of the momentum flux carried out by gravitational waves indicates that two distinct regimes are present in the post-merger phase: (i) an initial accelerated regime, followed by (ii) a deceleration regime in which the deceleration increases rapidly towards a maximum and then decreases to zero, when the gravitational wave emission ceases. The analysis is based on the Bondi-Sachs conservation law for the total momentum of the system. We obtain the total kick velocity ${V}_{k}$ imparted on the merged black hole during the accelerated regime (i) and the total antikick velocity ${V}_{mathrm{ak}}$ during the decelerated regime (ii), by evaluating the impulse of the gravitational wave flux during both regimes. The distributions of both ${V}_{k}$ and ${V}_{mathrm{ak}}$ as a function of the symmetric mass ratio $ensuremath{eta}$ satisfy a simple $ensuremath{eta}$-scaling law motivated by post-Newtonian analytical estimates. In the $ensuremath{eta}$-scaling formula the Newtonian factor is dominant in the decelerated regime, that generates ${V}_{mathrm{ak}}$, contrary to the behavior in the initial accelerated regime. For an initial infalling velocity $v/censuremath{simeq}0.462$ of each individual black hole we obtain a maximum kick ${V}_{k}ensuremath{simeq}6.4text{ }text{ }mathrm{km}/mathrm{s}$ at $ensuremath{eta}ensuremath{simeq}0.209$, and a maximum antikick ${V}_{mathrm{ak}}ensuremath{simeq}109text{ }text{ }mathrm{km}/mathrm{s}$ at $ensuremath{eta}ensuremath{simeq}0.205$. The net antikick velocity (${V}_{mathrm{ak}}ensuremath{-}{V}_{k}$) also satisfies a similar $ensuremath{eta}$-scaling law with a maximum approximately $102text{ }text{ }mathrm{km}/mathrm{s}$ also at $ensuremath{eta}ensuremath{simeq}0.205$, qualitatively consistent with results from numerical relativity simulations, and post-Newtonian evaluations of binary black hole inspirals. For larger values of the initial data parameter $v/c$ substantial larger values of the net antikick velocity are obtained. Based on the several velocity variables obtained, we discuss a possible definition of the center-of-mass motion of the merged system." @default.
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• W1990262032 date "2010-11-16" @default.
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• W1990262032 title "Kick processes in the merger of two colliding black holes" @default.
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• W1990262032 doi "https://doi.org/10.1103/physrevd.82.104033" @default.
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