Antikick Relation in High-Energy Head-On Collisions of Spinning Black Holes

Antikick Relation in High-Energy Head-On Collisions of Spinning Black Holes
Carlos O. Lousto (RIT), James Healy (RIT), Alessandro Ciarfella (RIT), Hiroyuki Nakano (Ryukoku University)
arXiv:2607.13018v1 Announce Type: cross
Abstract: The collision of black holes at relativistic speeds probes gravity in its most extreme dynamical regime. While the maximum gravitational recoil from emph{grazing} high-energy collisions ($approx28,562$~km/s, i.e., $sim0.1c$) and the maximum radiated energy $E_{rm rad}$ and remnant spin $alpha_f^{max}$ from such encounters ($E_{rm rad}/M_{rm ADM}approx32%$ where $M_{rm ADM}$ is the ADM mass, and $alpha_f^{max}approx0.987$) have been established previously~cite{Healy:2022jbh,Healy:2024lhl}, here we focus on the emph{head-on} high-energy collision of equal-mass spinning black holes and on the detailed structure of the resulting recoil. Performing a sequence of full numerical simulations for spin magnitudes $s=0.5,0.65$, and $0.8$ over a range of initial momenta $gamma v$, we characterize the peak recoil $V_p$, the final recoil $V_f$, and the antikick $Delta Vequiv V_f-V_p$, and we provide phenomenological fits of their dependence on $gamma v$ and $s$. We complement these results with a zero-frequency-limit (ZFL) analysis of the radiated energy and momentum, a quasinormal-mode model of the antikick, and a superposed boosted double-Kerr close-limit estimate. We find that in the relativistic regime ($gamma v>1$) the peak and final recoil are directly proportional, $V_papprox7.4,V_f$ (equivalently $Delta V approx-6.4,V_f$), largely independent of both the initial momentum and the spin magnitude, pointing to a common post-merger relaxation. While the ZFL predicts a leading linear-in-spin dependence, the close-limit analysis predicts a leading $s^3$ dependence of the recoil amplitude; with the three spin magnitudes studied here the empirical exponent is $s^{1.27pm0.08}$, motivating an even higher energy collision spin sequence study.arXiv:2607.13018v1 Announce Type: cross
Abstract: The collision of black holes at relativistic speeds probes gravity in its most extreme dynamical regime. While the maximum gravitational recoil from emph{grazing} high-energy collisions ($approx28,562$~km/s, i.e., $sim0.1c$) and the maximum radiated energy $E_{rm rad}$ and remnant spin $alpha_f^{max}$ from such encounters ($E_{rm rad}/M_{rm ADM}approx32%$ where $M_{rm ADM}$ is the ADM mass, and $alpha_f^{max}approx0.987$) have been established previously~cite{Healy:2022jbh,Healy:2024lhl}, here we focus on the emph{head-on} high-energy collision of equal-mass spinning black holes and on the detailed structure of the resulting recoil. Performing a sequence of full numerical simulations for spin magnitudes $s=0.5,0.65$, and $0.8$ over a range of initial momenta $gamma v$, we characterize the peak recoil $V_p$, the final recoil $V_f$, and the antikick $Delta Vequiv V_f-V_p$, and we provide phenomenological fits of their dependence on $gamma v$ and $s$. We complement these results with a zero-frequency-limit (ZFL) analysis of the radiated energy and momentum, a quasinormal-mode model of the antikick, and a superposed boosted double-Kerr close-limit estimate. We find that in the relativistic regime ($gamma v>1$) the peak and final recoil are directly proportional, $V_papprox7.4,V_f$ (equivalently $Delta V approx-6.4,V_f$), largely independent of both the initial momentum and the spin magnitude, pointing to a common post-merger relaxation. While the ZFL predicts a leading linear-in-spin dependence, the close-limit analysis predicts a leading $s^3$ dependence of the recoil amplitude; with the three spin magnitudes studied here the empirical exponent is $s^{1.27pm0.08}$, motivating an even higher energy collision spin sequence study.