Relativistic electromagnetism in rotating media

Authors: PIERRE HILLION

Abstract: This work concerns relativistic electromagnetism in a cylindrical Frenet-Serret frame. The tensor formalism of Maxwell's equations and electromagnetic fields in a vacuum is first developed in terms of cylindrical coordinates and afterwards applied to a rotating frame using the relativistic Trocheris-Takeno description of rotations. The metric ds^2 = g_{\mu \nu} dx^{\mu} dx^{\nu} of this frame is then obtained to find the determinant g of the g_{\mu \nu} matrix intervening in the relativistic Maxwell's equations, where the Greek indices take on the values 1,2,3,4. The propagation of harmonic cylindrical waves in rotating media is analyzed and it is shown that these waves can propagate only in some regions of spacetime. Geometrical optics and its paraxial approximation in rotating frames are also investigated in terms of a scalar field. Finally, the last section is devoted to electromagnetism in a rotating material medium with the use of covariant constitutive relations.

Keywords: Cylindrical frame, rotating medium, relativistic electromagnetism, metric tensor.

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