Photon Trajectories and Wavefront Structure Near a Black Hole

This work presents a self-contained theoretical analysis of photon propagation in the vicinity of a black hole, focusing on the geometrical structure of null geodesics, the role of unstable photon orbits, and the deformation of photon wavefronts in curved spacetime. By combining trajectory-based and wavefront-based descriptions, the paper provides a unified interpretation of black hole optics, clarifying how photon trapping near the photon sphere organizes light propagation and gives rise to observable features such as light rings, shadow boundaries, and strong-field gravitational lensing. Special emphasis is placed on wavefront deformation, folding, and caustic formation near the critical impact parameter. These collective geometrical effects naturally explain the sharpness and robustness of black hole shadows and surrounding brightness enhancements, independent of specific emission models. The analysis is based entirely on the established framework of general relativity and does not introduce new metric solutions or modifications of gravity. The results offer a clear conceptual bridge between spacetime geometry and observable signatures, supporting the interpretation of current and future black hole imaging and lensing observations. This version represents an updated and refined release intended for broad dissemination and citation.