Photon ring structure of rotating regular black holes and no-horizon spacetimes
Abstract
The Kerr black holes possess a photon region with prograde and retrograde orbits radii, respectively, M≤ rp-≤ 3M and 3M≤ rp+≤ 4M, 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 , gE such that =0 has no zeros for g > gE, one double zero at r = rE for g = gE , 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 gE< g ≤ gc, e.g., for a=0.10M, Bardeen (gE=0.763332M<g≤ gc= 0.816792M), Hayward (gE=1.05297M < g≤ gc = 1.164846M) and nonsingular (gE=1.2020M < g ≤ gc= 1.222461M) 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 C for the three no-horizon rotating spacetimes satisfy C≤ 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.