High-Order Photon Rings around Kerr Naked Singularities

TL;DR

This study addresses the challenge of testing strong-field GR by distinguishing Kerr naked singularities (KNS) from Kerr black holes using horizon-scale imaging. It combines 3D GRMHD simulations with general-relativistic radiative transfer to predict the high-order photon-ring structure around a rapidly spinning KNS with a=1.01 and to compute corresponding VLBI observables at 230 GHz. The results reveal cascaded photon rings that exist both outside and inside the nominal shadow, with an inclination- and order-dependent gap that alters visibility signatures relative to Kerr black holes; these features persist across horizon-scale baselines and offer a concrete observational route for testing the presence of an event horizon with future missions like BHEX. The work provides predictive templates for horizon-scale tests of strong-field GR and highlights the need for longer baselines and realistic emission modeling to decisively rule out horizonless spacetimes.

Abstract

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.

Figures (3)

• Figure 1: High-Order Photon ring structure around a KNS with spin $a = 1.01$ and a polar inclination angle $i = 60^\circ$, ray-traced from 3D GRMHD simulation data from NKSGRMHD2025ApJ...978...44D. The critical curve is calculated with the analytical calculations (Equations \ref{['eq:Phi']}-\ref{['eq:r_ph']}). Multiple cascaded photon rings appear on both sides of the critical curve (blue) due to the absence of an event horizon. Inner rings are thicker and more sparse, connected with outer rings around the equatorial plane. Intensity is normalized and visualized on a quadratic scale to enhance the visibility of the sub-ring. Dark regions on the right side are likely artifacts from the numerical boundary in the simulation and do not affect the analysis of the VLBI observational signature.
• Figure 2: Decomposition of the sub-rings at different inclinations. Two cascaded rings per order of photon ring appear on both sides of the critical curve. For all inclination angles, rings inside the critical curve have a thicker profile than those outside. At the higher inclination angles, high-order photon rings begin to open a gap. The right panels display the spatial contribution of each sub-ring to the total image. Similar to KBH, the intensity decreases as the order of the photon ring increases, but the presence of inner rings introduces additional structure within the shadow region.
• Figure 3: Normalized visibility amplitude of KNS ($a=1.01$) as a function of $(u, v)$-distance for five inclination angles, shown from top to bottom. Each curve represents the amplitude from cascaded sub-rings. The absence of an event horizon produces a thicker emission structure, resulting in similar decay rates of the visibility amplitude across sub-rings compared to the sharper fall-off seen in that of black holes.