AI 中文总结
本研究计算轻重致密天体引力冲击波碰撞的高频引力波辐射，通过冲击波传播子得到潮汐响应函数形式解，分析微扰展开各阶贡献并验证软极限简化，同时关联杨-米尔斯碰撞的二重拷贝结构与程函散射框架。
AI 中文摘要
我们计算了能量为$μ_L$的轻质量致密天体与能量为$μ_H \gg μ_L$的重致密天体（黑洞）发生冲击波碰撞时的高频引力波辐射。我们通过冲击波传播子得到了形式解，这些传播子给出了$O(μ_Lμ_H^n)$阶潮汐响应函数的快照，这类响应对黑洞形成的经典动力学以及潜在的半经典动力学十分敏感。在微扰展开中，首个非平凡的$O(μ_Lμ_H)$阶贡献来自两个雷吉化引力子融合产生的Lipatov顶点发射的一个引力子。当引力子频率$\omega\rightarrow 0$时，Lipatov振幅退化为单引力子交换的Weinberg振幅的极端相对论极限。在$O(μ_Lμ_H^2)$阶，Lipatov振幅包含两部分：一部分对应引力子与一个雷吉化引力子的再散射，另一部分对应三个雷吉化引力子融合的顶点发射的引力子。这些非平凡贡献在软极限下同样简化为双引力子交换的Weinberg辐射振幅。我们全程强调了该结果与杨-米尔斯冲击波稀-密碰撞中胶子辐射的二重拷贝结构的关联，并将本次冲击波研究结果与Veneziano等人的程函多次散射框架建立了联系。
英文摘要
We compute high frequency gravitational wave radiation in shockwave collisions of a light mass compact object with energy $μ_L$ off a heavy compact object (black hole) with energy $μ_H \gg μ_L$. A formal solution is obtained in terms of shockwave propagators that provide snapshots of $O(μ_Lμ_H^n)$ tidal response functions sensitive to classical and potentially semi-classical dynamics of black hole formation. In a perturbative expansion, the first nontrivial contribution of $O(μ_Lμ_H)$ is the emission of a graviton from the Lipatov vertex generated by the fusion of two reggeized gravitons. For graviton frequencies $ω\rightarrow 0$, the Lipatov amplitude reduces to the ultrarelativistic limit of the single-graviton exchange Weinberg amplitude. At $O(μ_Lμ_H^2)$, the Lipatov amplitude includes a piece accounting for the rescattering of the graviton off a reggeized graviton and another, corresponding to graviton emission from a vertex fusing three reggeized gravitons. These nontrivial contributions again simplify to the Weinberg radiative amplitude for two-graviton exchange in the soft limit. We highlight throughout double copy structures to gluon radiation in dilute-dense collisions of Yang-Mills shockwaves. We relate our shockwave results to the eikonal multiple scattering framework of Veneziano et al.
Comments50 pages, 13 figures
