Electromagnetic variations in curved space-times

The concept of a static index of refraction is being used to demonstrate that the quantities describing the vibrational ellipse vary because of the torsion induced by the index of refraction. Further, the idea is exploited that in relativistic objects such variations can be induced by the non-Euclidean character of the external geometry. Expressions are given for the induced curvature and torsion and, finally the Hamilton-Jacobi equation is used to derive the effective index of refraction for Kerr's geometry.