Correspondence between multileaf topology of closed geodesics and spatiotemporal autocorrelations of hotspot images in Schwarzschild spacetime
Abstract
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 Nband and recurrence points Nrec. The integers are recovered as z=Nrec−1, w=⌊ (Nband+1)/(Nrec−1)⌋−1, and v=(Nband+1)bmod(Nrec−1). Here, ⌊ x⌋ 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.
Related
- Particle geodesics, shadows and accretion disk luminosity of a Dehnen (1,4,5/2)-Schwarzschild black hole
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BibTeX
@misc{xie2026correspondence,
title = {{Correspondence between multileaf topology of closed geodesics and spatiotemporal autocorrelations of hotspot images in Schwarzschild spacetime}},
author = {Fengting Xie and Qing-Hua Zhu and Xin Li},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.36767},
eprint = {2609.36767},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.36767},
}
RIS
TY - UNPB
TI - Correspondence between multileaf topology of closed geodesics and spatiotemporal autocorrelations of hotspot images in Schwarzschild spacetime
AU - Fengting Xie
AU - Qing-Hua Zhu
AU - Xin Li
PY - 2026
DA - 2026/09/29
PB - arXiv
DO - 10.48550/arxiv.2609.36767
UR - https://arxiv.org/abs/2609.36767
AB - 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_band and recurrence points N_rec. The integers are recovered as z=N_rec−1, w=⌊ (N_band+1)/(N_rec−1)⌋−1, and v=(N_band+1)bmod(N_rec−1). Here, ⌊ x⌋ 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.
ER -