Gravitational recoil in nonspinning black hole binaries: the span of test-mass results

Abstract

We consider binary systems of coalescing, nonspinning, black holes of masses $m_1$ and $m_2$ and show that the gravitational recoil velocity for any mass ratio can be obtained accurately by extrapolating the waveform of the test-mass limit case. The waveform obtained in the limit $m_1/m_2\ll 1$ via a perturbative approach is extrapolated in $\nu =m_1{m}_2/(m_1+m_2{)}^2$ multipole by multipole using the corresponding, analytically known, leading-in-$\nu$ behavior. The final kick velocity computed from this $\nu$-flexed waveform is written as $v(\nu )/c=0.04457{\nu }^2\sqrt{1-4\nu }(1-2.07106\nu +3.93472{\nu }^2-4.78404{\nu }^3+2.52040{\nu }^4)$ and is compatible with the outcome of numerical relativity simulations

5 pages, 3 figures. Matches published version

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