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Non-covariance and unfaithfulness in projective spacetime transformation optics

Developments in Transformation Optics (TO) have drawn heavily on ideas from general relativity. This motivates a line of inquiry that seeks a deeper, more rigorous understanding of the spacetime covariant formulation of electrodynamics in media, and generalized ideas from general relativity that can further enhance TO. We show that basing TO on the idea of metric transformations is not covariant and introduces distortions to the desired behaviour of a light beam, but that these issues can be resolved by keeping the metric fixed.