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It is known that vacuum Maxwell equations being considered on the background of
any pseudo-Riemannin 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. We
have proved that in all the examined cases, effective tensors and of electric permittivity
εij(x)
and magnetic permeability µij(x) obey one the same condition:
εij(x)µjk(x)=δik.
Expressions for tensors εij(x) and µjk(x) are simple,
but this simplicity is misleading. For
each curved space-time model we are to solve Maxwell equations separately and anew. We
have constructed the solutions, applying Maxwell equations in spinor form.
Keywords: constitutive relations, electrodynamics, geometrical modeling, Maxwell equations, Riemannian space-time, spherical and cylindric symmetry, spinor formalism |
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