The Kerr black holes possess a photon region with prograde and retrograde orbits radii, respectively, and , and thereby always cast a closed photon ring or a shadow silhouette for a ⩽ M. For a > M, it is a no-horizon spacetime (naked singularity) wherein prograde orbits spiral into the central singularity, and retrograde orbits produce an arc-like shadow with a dark spot at the center. We compare Kerr black holes’ photon ring structure with those produced by three rotating regular spacetimes, viz Bardeen, Hayward, and nonsingular. These are non-Kerr black hole metrics with an additional deviation parameter of g related to the nonlinear electrodynamics charge. It turns out that for a given a, there exists a critical value of g, g _E such that Δ = 0 has no zeros for g > g _E, one double zero at r = r _E for g = g _E, respectively, corresponding to a no-horizon regular spacetime and extremal black hole with degenerate horizon. We demonstrate that, unlike the Kerr naked singularity, no-horizon regular spacetimes can possess closed photon ring when g _E < g ⩽ g _c, e.g. for a = 0.10M, Bardeen (g _E = 0.763 332M < g ⩽ g _c = 0.816 792M), Hayward (g _E = 1.052 97M < g ⩽ g _c = 1.164 846M) and nonsingular (g _E = 1.2020M < g ⩽ g _c = 1.222 461M) no-horizon spacetimes have closed photon ring. These results confirm that the mere existence of a closed photon ring does not prove that the compact object is necessarily a black hole. The ring circularity deviation observable ΔC for the three no-horizon rotating spacetimes satisfy ΔC ⩽ 0.10 as per the M87^* black hole shadow observations. We have also appended the case of Kerr–Newman no-horizon spacetimes (naked singularities) with similar features.

克尔黑洞具有分别具有顺行和逆行轨道半径的光子区域，并且因此总是投射出一个闭合的光子环或一个⩽ M的阴影轮廓。对于a > M，它是一个无视界时空（裸奇点），其中顺行轨道螺旋进入中心奇点，逆行轨道产生中心有黑点的弧形阴影。我们将克尔黑洞的光子环结构与由三个旋转的规则时空（即 Bardeen、Hayward 和 nonsingular）产生的光子环结构进行比较。这些是非克尔黑洞度量，具有额外的偏差参数g与非线性电动力学电荷有关。事实证明，对于给定的 a，存在一个临界值g，g _E使得 Δ = 0 对于g > g _E没有零，对于g = g _E在r = r _E有一个双零，分别对应于到一个无视界规则时空和具有退化视界的极端黑洞。我们证明，与克尔裸奇点不同，当g _E < g ⩽ g _c时，无视界规则时空可以拥有闭合光子环，例如 a = 0.10 M , Bardeen ( g _E = 0.763 332 M < g ⩽ g _c = 0.816 792 M ), Hayward ( g _E = 1.052 97 M < g ⩽ g _c = 1.164 846 M ) 和非奇异的 ( g _E = 1.2020 M < g ⩽ g _c = 1.222 461 M) 无视界时空有闭合的光子环。这些结果证实，仅仅存在闭合光子环并不能证明致密物体一定是黑洞。^{根据 M87 *}黑洞阴影观测，三个无视距旋转时空的可观测环圆度偏差 ΔC满足ΔC ⩽ 0.10 。我们还附加了具有相似特征的 Kerr-Newman 无视界时空（裸奇点）案例。