Fermat's principle and variational analysis of an optical model for light propagation exhibiting a critical radius

Fermat's principle and variational analysis is used to analyze the trajectories of light propagating in a radially inhomogeneous medium with a singularity in the center. It is found that the light trajectories are similar to those around a black hole, in the sense that there exists a critical radius within which the light cannot escape, but spirals into the singularity.