Spinor Maxwell Equations in Riemannian Space-Time and Modeling Constitutive Relations in Electrodynamics

Abstract

It is known that vacuum Maxwell equations being considered on the background of any pseudo-Riemannian space-time may be interpreted as Maxwell equations in Minkowski space but specified in some effective medium, which constitutive relations are determined by metric of the curved space-time. In that context, we have considered de Sitter, anti de Sitter, and Schwarzschild models. Also we have studied hyperbolic Lobachevsky and spherical Riemann models, parameterized by coordinates with spherical or cylindric symmetry.