AI 中文总结
研究等质量旋转黑洞高能正面碰撞的反冲关系，通过全数值模拟刻画相关物理量，给出其对初始动量和自旋大小的依赖关系，发现相对论 regime中峰值与最终反冲成正比，还对比不同模型预测，为更高能量碰撞自旋序列研究提供依据。
AI 中文摘要
黑洞以相对论速度碰撞可在最极端动力学状态下探测引力。此前已确定掠射高能碰撞的最大引力反冲（约28562千米/秒，即约0.1c）、此类碰撞的最大辐射能量\(E_{\rm rad}\)和残余自旋\(\alpha_f^{\max}\)（\(E_{\rm rad}/M_{\rm ADM}\approx32\%\)，\(M_{\rm ADM}\)为ADM质量，\(\alpha_f^{\max}\approx0.987\)）。本文聚焦等质量旋转黑洞的高能正面碰撞及反冲的详细结构。通过对自旋大小\(s = 0.5,0.65,0.8\)在一系列初始动量\(\gamma v\)下进行全数值模拟，刻画了峰值反冲\(V_p\)、最终反冲\(V_f\)和反踢\(\Delta V\equiv V_f - V_p\)，并给出它们对\(\gamma v\)和\(s\)依赖关系的唯象拟合。还通过辐射能量和动量的零频率极限分析、反踢的准正则模模型及叠加增强双克尔近极限估计对结果进行补充。发现在相对论 regime（\(\gamma v>1\)）中，峰值和最终反冲成正比，\(V_p\approx7.4V_f\)（等价于\(\Delta V \approx - 6.4V_f\)），很大程度上与初始动量和自旋大小无关，表明存在共同的合并后弛豫。零频率极限预测反冲幅度与自旋呈线性依赖，近极限分析预测为\(s^3\)依赖；本文研究的三个自旋大小下经验指数为\(s^{1.27\pm0.08}\)，促使开展更高能量碰撞自旋序列研究。
英文摘要
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 $α_f^{\max}$ from such encounters ($E_{\rm rad}/M_{\rm ADM}\approx32\%$ where $M_{\rm ADM}$ is the ADM mass, and $α_f^{\max}\approx0.987$) 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 $γv$, we characterize the peak recoil $V_p$, the final recoil $V_f$, and the antikick $ΔV\equiv V_f-V_p$, and we provide phenomenological fits of their dependence on $γv$ 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 ($γv>1$) the peak and final recoil are directly proportional, $V_p\approx7.4\,V_f$ (equivalently $ΔV \approx-6.4\,V_f$), 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 $s^{1.27\pm0.08}$, motivating an even higher energy collision spin sequence study.
Comments9 pages, 5 figures, 3 tables
