Kerr-Degenerate Shadows and Distinct Strong-Deflection Lensing in Rotating Hayward-like and Bardeen-like Geometries

Abstract

We study and compare rotating Hayward-like and Bardeen-like geometries within a common Kerr-like axisymmetric ansatz, with the models distinguished by their areal-radius functions $R_i(ρ)$. On the adopted radial branches, the positive minimum areal radius excludes the Kerr ring locus, and the curvature invariants examined here remain finite. We identify the parameter domains containing two, one, or no horizons. The two geometries have the same asymptotic Komar charges but different finite-radius values. If we treat the Einstein tensor as an effective stress tensor, then for every nonzero regularity length $\ell$, this ansatz violates the null and weak energy conditions, as demonstrated by the equatorial radial-null contraction. For the complete photon family on a black-hole branch, the shadow boundary is identical to that of Kerr at the same mass, spin, and observer inclination, and is also identical for the two regular geometries. The corresponding area-equivalent shadow diameters for M87* and Sgr~A* are consistent with the approximate Event Horizon Telescope (EHT)-based intervals adopted here, and we do not obtain further constraints on $\ell$. By contrast, the prograde equatorial strong-deflection limit (SDL) calculations are only partly degenerate. At fixed spin, $u_m^+$ and $θ_\infty^+$ are common to Kerr and the two regular geometries, whereas $\bar a_+$, $\bar b_+$, the image separation, the relative magnitude, and the subleading time-delay correction depend on $\ell$ and on the areal-radius profile. Within the stated strong-deflection approximation, future measurements of $ΔT_{2,1}$, $s^+$, and $r_{\rm mag}^+$ may help test these rotating geometries and distinguish the Hayward-like and Bardeen-like predictions from Kerr, including in the one-horizon parameter domain where the adopted branch contains no Kerr-like inner horizon.