General relativistic contributions in transformation optics

One potentially realistic specification for devices designed with transformation optics is that they operate with high precision in curved space–time, such as Earth orbit. This raises the question of what, if any, role does space–time curvature play in determining transformation media? Transformation optics has been based on a 3-vector representation of Maxwell's equations in flat Minkowski space–time. I discuss a completely covariant, manifestly four-dimensional approach that enables transformations in arbitrary space–times, and demonstrate this approach for stable circular orbits in the spherically symmetric Schwarzschild geometry. Finally, I estimate the magnitude of curvature induced contributions to satellite-borne transformation media in Earth orbit and comment on the level of precision required for metamaterial fabrication before such contributions become important