Linear media in classical electrodynamics and the Post constraint

The Maxwell equations are formulated in a generally covariant and metric-free way in 1+3 and subsequently in 4 dimensions. For this purpose, we use the excitations D, H and the field strengths E,B. A local and linear constitutive law between excitations and field strengths is assumed, with a constitutive tensor of 36 components. The properties of this tensor are discussed. In particular, we address the validity of the Post constraint. In this connection, the Tellegen gyrator, the axion field, and the “perfect electromagnetic conductor” of Lindell and Sihvola are compared with each other.