Maxwell equations in Riemannian space-time, geometry effect on material equations in media
Abstract
The known possibility to consider the (vacuum) Maxwell equations in a curved space-time as Maxwell equations in flat space-time(Mandel'stam L.I., Tamm I.E.) taken in an effective media the properties of which are determined by metrical structure of the curved model is studied. Metrical structure of the curved space-time generates effective constitutive equations for electromagnetic fields, the form of four corresponding symmetrical tensors is found explicitly for general case of an arbitrary Riemannian space - time. Four constitutive tensors are not independent and obey some additional constraints between them. Several simple examples are specified in detail:itis given geometrical modeling of the anisotropic media (magnetic crystals) and the geometrical modeling of a uniform media in moving reference frame in the Minkowsky electrodynamics -- the latter is realized trough the use of a non-diagonal metrical tensor determined by 4-vector velocity of the moving uniform media. Also the effective material equations generated by geometry of space of constant curvature (Lobachevsky and Riemann models) are determined.
Cite
@article{arxiv.0709.2415,
title = {Maxwell equations in Riemannian space-time, geometry effect on material equations in media},
author = {V. M. Red'kov and N. G. Tokarevskaya and E. M. Bychkouskaya and George J. Spix},
journal= {arXiv preprint arXiv:0709.2415},
year = {2011}
}
Comments
14 pages, Report to: XIV Annual Seminar Nonlinear Penomena in Complex Systems. Minsk, May 22-25, 2007