High-Order Photon Rings around Kerr Naked Singularities

We present a detailed study of higher-order photon rings of an accreting Kerr naked singularity (KNS) with dimensionless spin parameter $a=1.01$; i.e., a horizonless, overly spinning compact object. Motivated by horizon-scale very-long-baseline interferometry (VLBI) including Event Horizon Telescope (EHT) and future missions such as the Black Hole Explorer (BHEX), we analyze image morphology and interferometric visibilities to identify observational signatures that differentiate KNS from Kerr black holes. We find that higher-order photon rings are tightly concentrated within the nominal ``shadow'' region and that the shadow develops a pronounced gap at sufficiently large observer inclination. These morphological differences produce measurable deviations in the complex visibilities relative to Kerr black hole predictions. Our results indicate that photon-ring structure and visibility-domain diagnostics at horizon-resolving baselines can provide a direct observational test of the presence (or absence) of an event horizon and thus offer a concrete avenue to test general relativity with future horizon-scale observations.