A proposal to test the distinguishability of singular and regular black holes using a GRIN lens analogue

We develop a theoretical framework for emulating {blue}{selected critical features of} the null geodesics of spherically symmetric static black holes using a cylindrical graded-index (GRIN) lens. {blue}{By comparing the radial turning-point conditions for light rays and null geodesics,} we recover the isotropic radial refractive-index profile \(n(r)=1/√f(r)\), {blue}{which reproduces the photon-sphere radius and critical impact parameter but not the complete projected trajectories.} Building upon this established correspondence, we perform a quantitative comparison between the Schwarzschild geometry and the regular Hayward metric, and extend the analysis to the Bardeen, {blue}{Dymnikova}, and Simpson--Visser regular black-hole models. {blue}{For representative regularization parameters, the shift in the critical impact parameter is strongly model dependent and can even vanish, as occurs for the Simpson--Visser black-hole branch.} In the experimentally accessible region, where the refractive index remains below \(~ 2\), the Hayward profile considered here produces a shift in the {blue}{full} shadow width of \(1.8\)~cm relative to Schwarzschild. The comparison with other regular geometries shows that such optical deviations are not specific to the Hayward model and suggests that precision measurements of the shadow displacement could provide a means of discriminating between different regular black-hole models. {blue}{However, regularization does not generically imply a nonzero shadow displacement.} The proposed GRIN-lens platform therefore provides a controlled laboratory setting for investigating strong-field gravitational phenomena, including critical capture and shadow formation, and establishes quantitative benchmarks for future high-precision experiments.