发表机构
Chongqing University（重庆大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本研究通过光线追踪构建Schwarzschild黑洞周围闭合测地线热点图像的自相关，建立拓扑整数与相关带数及递归点数的定量对应，从而从图像自相关恢复轨道拓扑。
AI 中文摘要
相对论性闭合轨道按其多叶结构的分类为研究强场动力学提供了一个框架。在天文图像中识别这些结构仍然具有挑战性。利用光线追踪，我们构造了围绕Schwarzschild黑洞沿有界闭合测地线运动的点状热点的主图像的时空自相关。这些轨道由三个整数$(z,w,v)$分类，其中$z$计数叶数，$w$计数每个径向周期内的额外回旋数，$v$指定轨道叶被追踪的顺序。对于所研究的轨道族，我们的数值结果建立了拓扑整数$(z,w,v)$与相关带数$N_{\rm band}$和递归点数$N_{\rm rec}$之间的对应关系。这些整数被恢复为$z=N_{\rm rec}-1$，$w=\left\lfloor (N_{\rm band}+1)/(N_{\rm rec}-1)\right\rfloor-1$，以及$v=(N_{\rm band}+1)\bmod(N_{\rm rec}-1)$。这里，$\lfloor x\rfloor$表示不超过$x$的最大整数，$\bmod$表示取余运算。这些关系提供了一种从热点图像自相关中恢复闭合轨道拓扑的定量方法。
英文摘要
The classification of relativistic closed orbits by their multileaf structures provides a framework for studying strong-field dynamics. Identifying these structures in astronomical images remains challenging. Using ray tracing, we construct the spatiotemporal autocorrelations of the primary image of a pointlike hotspot moving along bound closed geodesics around a Schwarzschild black hole. These orbits are classified by three integers $(z,w,v)$, where $z$ counts the leaves, $w$ counts the additional whirls during each radial period, and $v$ specifies the order in which the orbital leaves are traced. For the orbit families examined, our numerical results establish a correspondence between the topological integers $(z,w,v)$ and the numbers of correlation bands $N_{\rm band}$ and recurrence points $N_{\rm rec}$. The integers are recovered as $z=N_{\rm rec}-1$, $w=\left\lfloor (N_{\rm band}+1)/(N_{\rm rec}-1)\right\rfloor-1$, and $v=(N_{\rm band}+1)\bmod(N_{\rm rec}-1)$. Here, $\lfloor x\rfloor$ denotes the greatest integer not exceeding $x$, and $\bmod$ denotes the remainder operation. These relations provide a quantitative method for recovering closed-orbit topology from hotspot image autocorrelations.
Comments20 pages, 10 figures
