Relativity and refraction

[moth]

Is it possible to model refraction using General Relativity ?
If you assume local speed of light inside a low refractive index material to be c, and find the length contraction and time dilation for an "outside observer",could you work out the local curvature?

[Klaynos]

A few of my friends work on this. You'll want to look up transformation optics. Here's a paper I recall uses the process:

 

http://www.opticsinfobase.org/ol/abstract.cfm?uri=ol-36-22-4311

 

You use refractive indices etc... as causing space to curve.

[moth]

Thanks Klaynos. Transformation optics googled up some interesting looking stuff on arxiv.