Photon ring structure of rotating regular black holes and no-horizon spacetimes

The Kerr black holes possess a photon region with prograde and retrograde orbits radii, respectively, $M\leq r_p^-\leq 3M$ $3M\leq r_p^+\leq 4M$, thereby always cast closed ring or shadow silhouette for $a\leq M$. For $a>M$, it is no-horizon spacetime (naked singularity) wherein spiral into the central singularity, produce an arc-like dark spot at center. We compare holes' structure those produced by three rotating regular spacetimes, viz. Bardeen, Hayward, nonsingular. These are non-Kerr hole metrics additional deviation parameter of $g$ related to nonlinear electrodynamics charge. It turns out that given $ $, there exists critical value g $g_E$ such $\Delta=0$ has no zeros > g_E$, one double zero r = r_E g_E corresponding extremal degenerate horizon. demonstrate that, unlike naked spacetimes can when $g_E< \leq g_c$, e.g., $a=0.10M$, Bardeen ($g_E=0.763332M<g\leq g_c= 0.816792M$), Hayward ($g_E=1.05297M < g\leq g_c 1.164846M$) nonsingular ($g_E=1.2020M 1.222461M$) have ring. results confirm mere existence does not prove compact object necessarily hole. circularity observable $\Delta C$ satisfy C\leq 0.10$ as per M87* observations. also appended case Kerr-Newman singularities) similar features.