Breaking the degeneracy among regular black holes with gravitational lensing

Abstract: We examine parameter degeneracies in Culetu, Bardeen and Hayward regular black holes across lensing, shadow and quasinormal mode regimes. Our analysis reveals that while Einstein ring data yield extremely loose constraints, with the regularization parameter $q$ exceeding $\mathcal{O}(10<sup>3)$, they fail to improve the parameter estimation when combined with strong lensing observables. In contrast, the Event Horizon Telescope observations provide remarkably tight limits: $0 \leq q &lt; 0.0466 &lt;0.0847$ for Culetu, $0 \leq q &lt; 0.5115 &lt;0.6682$ for Bardeen and $0 \leq q &lt; 1.0258 &lt;1.1881$ for Hayward, which shows that the strong field regime alone dominates the available parameter space. Despite these bounds, leading order geometric observables remain highly degenerate, which masks the microscopic details of non-singular cores. To break this ``macroscopic universality,'' we identify high order signatures, such as the Lyapunov exponent and subleading time delays, as sensitive probes of near horizon curvature. Crucially, we discover that the brightness hierarchy of accretion induced intensity profiles undergoes a fundamental inversion when transitioning from lensing dominated static flows to dynamics dominated infalling flows. These results demonstrate that high resolution temporal and intensity profiles are essential for distinguishing between regular black hole geometries.