Stabilizing General Relativity Null Geodesics: A Multi-Ray AMDCF Simulation of the Einstein Ring

The bending of light around massive objects (gravitational lensing) is described by the null geodesics of General Relativity. Numerical integration of these trajectories near a singularity often leads to catastrophic computational blow-up. In this paper, we upgrade our previous Newtonian model to a rigorous post-Newtonian approximation of General Relativity. We simulate a bundle of parallel light rays interacting with a massive lens using the 4/r^3 curvature term. While the unprotected rays plunge into the singularity and diverge, the AMDCF (Adaptive Memory-Driven Coupling Framework) dynamic safety valve bounds the effective curvature at the core. This allows the rays to bend sharply and converge at the focal point, successfully reproducing the theoretical Einstein Ring without numerical failure. This work demonstrates the universality of the AMDCF framework in handling extreme nonlinearities in astrophysics.