How spacetime deformations reshape light and shadows: a numerical study of photon orbits and observable shadow size

We study how a one-parameter deformation of an effective spherically symmetric spacetime affects the structure of null circular geodesics and the resulting observable shadow of a compact object. The geometry is controlled by a deformation parameter β = r0/rs, which continuously modifies the effective potential governing light propagation. We show that the system exhibits a critical transition in which photon sphere solutions exist for β < βmax and disappear via a saddle node bifurcation at βmax ≈ 0.60942. Despite this sharp geometric transition, the observable shadow size evolves smoothly and deviates only weakly from the Schwarzschild value, with a maximum relative change of approximately 3.6%.