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

摘要

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