Spacetime Deformations and Electromagnetism in Material Media

This paper is intended to investigate the relation between electrodynamics in anisotropic material media and its analogous formulation in an spacetime, with non-null Riemann curvature tensor. After discussing the electromagnetism via chiral differential forms, we point out the optical activity of a given material medium, closely related to topological spin, and the Faraday rotation, associated to topological torsion. Both quantities are defined in terms of the magnetic potential and the electric and magnetic fields and excitations. We revisit some properties of material media and the associated Green dyadics. Some related features of ferrite are also investigated. It is well-known that the constitutive tensor is essentially equivalent to the Riemann curvature tensor. In order to investigate the propagation of electromagnetic waves inmaterial media, we prove that it is analogous to consider the electromagnetic wave propagation in the vacuum, but this time in a curved spacetime, which is obtained by a deformation of the Lorenztian metric of Minkowski spacetime. Spacetime deformations leave invariant the form of Maxwell equations. Also, there exists a close relation between Maxwell equations in curved spacetime and in an anisotropic material medium, indicating that electromagnetism and spacetime properties are deeply related. For instance, the equations of holomorphy in Minkowski spacetime are essentially Maxwell equations in vacuum. Besides, the geometrical aspects of wave propagation can be described by an effective geometry which represents a modification of the Lorentzian metric of Minkowski spacetime, i.e., a kind of spacetime deformation.