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We performed a series of 1381 full numerical simulations of high energy collision of two black holes to search for the maximum recoil velocity after their merger. We studied equal mass binaries with opposite spins pointing along the orbital plane to maximize asymmetric gravitational radiation and performed a search of spin orientations in the plane, impact parameters, and initial linear momenta to find a maximum recoil velocity extrapolated to the extreme spinning case of [Formula: see text][Formula: see text]km/s, thus tightly bounding recoil by [Formula: see text] the speed of light. 

Abstract We explicitly demonstrate that current numerical relativity techniques are able to accurately evolve black hole binaries with mass ratios of the order of 1000:1. This proof of principle is relevant for future third generation gravitational wave detectors and space mission LISA, as by purely numerical methods we would be able to accurately compute gravitational waves from the last stages of black hole mergers, as directly predicted by general relativity. We perform a sequence of simulations in the intermediate to small mass ratio regime, m 1 p / m 2 p = 1 / 7 , 1 / 16 , 1 / 32 , 1 / 64 , 1 / 128 , 1 / 256 , 1 / 512 , 1 / 1024 , with the small hole starting from rest at a proper distance D ≈ 13 M . We compare these headon full numerical evolutions with the corresponding semianalytic point particle perturbative results finding an impressive agreement for the total gravitational radiated energy and linear momentum as well as for the waveform spectra. We display numerical convergence of the results and identify the minimal numerical resolutions required to accurately solve for these very low amplitude gravitational waves. This work represents a first step towards the considerable challenge of applying numerical-relativity waveforms to interpreting gravitational-wave observations by LISA and next-generation ground-based gravitational-wave detectors.