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Antikick relation in high-energy head-on collisions of spinning black holes

Carlos O. Lousto1, James Healy1, Alessandro Ciarfella1, and Hiroyuki Nakano2

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Phys. Rev. D 114, 084013 – Published 5 October, 2026

DOI: https://doi.org/10.1103/7z7t-dsmk

Abstract

The collision of black holes at relativistic speeds probes gravity in its most extreme dynamical regime. We study head-on collisions of equal-mass black holes whose spins are antialigned with each other and perpendicular to the collision axis: the minimal configuration in which a net gravitational recoil is generated, purely spin driven and, by symmetry, one dimensional. Performing a sequence of full numerical simulations for dimensionless spin magnitudes χ=0.5, 0.65, and 0.8 over a wide range of initial momenta, we follow the recoil velocity accumulated in time: it rises to a peak value Vp at merger and then relaxes to a smaller final value Vf—an “antikick”, during which the direction of the emitted linear momentum reverses. In the relativistic regime, the peak and final recoils are found to be directly proportional, Vp≈7.4Vf, largely independently of both the initial momentum and the spin magnitude, pointing to a common postmerger relaxation. The antikick amplitude collapses onto a single master curve with an empirical spin scaling χ1.27±0.08, intermediate between the linear dependence predicted by a zero-frequency-limit analysis and the cubic dependence of a close-limit estimate, both derived in the Appendixes together with a quasinormal-mode model of the antikick. These results complement the previously established maxima of recoil and radiated energy from grazing high-energy encounters [J. Healy and C. O. Lousto, Phys. Rev. Lett. 131, 071401 (2023)., J. Healy, A. Ciarfella, and C. O. Lousto, Phys. Rev. D 111, 084077 (2025).] and motivate sequences at higher spins and energies.

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Phys. Rev. D 114, 084013– Published 5 October, 2026
  • Received 14 July 2026
  • Accepted 11 September 2026
Article part of CHORUS
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