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, $M\le r_p^{-}\le 3M$ and $3M\le r_p^{+}\le 4M$, and thereby always cast a closed photon ring or a shadow silhouette for $a\le M$. 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 $\Delta =0$ 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 $g_E<g\le g_c$, e.g., for $a=0.10M$, Bardeen ($g_E=0.763332M<g\le g_c=0.816792M$), Hayward ($g_E=1.05297M<g\le g_c=1.164846M$) and nonsingular ($g_E=1.2020M<g\le g_c=1.222461M$) 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 $\Delta C$ for the three no-horizon rotating spacetimes satisfy $\Delta C\le 0.10$ 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.

20 pages, 18 figures and 6 tables. Title modified, references and discussions added. Matches the published version in CQG

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