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It is commonly assumed that if the optical metric of a dielectric medium isidentical to the metric of a vacuum space-time then light propagation throughthe dielectric mimics light propagation in the vacuum. However, just as thecurved surface of the Earth cannot be mapped into a flat plane withoutdistortion of some surface features, so too is it impossible to project thebehavior of light from the vacuum into a dielectric analog residing inMinkowski space-time without introducing distortions. We study the covarianceproperties of dielectric analog space-times and the kinematics of a congruenceof light in the analog, and show how certain features can be faithfullyemulated in the analog depending on the choice of projection, but that not allfeatures can be simultaneously emulated without distortion. These findingsindicate conceptual weaknesses in the idea of using analog space-times as abasis for transformation optics, and we show that a certain formulation oftransformation optics closely related to analog space-times resolves theseissues.

Cartographic distortions make dielectric spacetime analog models imperfect mimickers