Nonlinear Phenomena in Complex Systems, 2014, Vol.17, No.1, pp.17-39

NONLINEAR PHENOMENA IN COMPLEX SYSTEMS
An Interdisciplinary Journal

2014, Vol.17, No.1, pp.17-39

Electromagnetic Field on de Sitter Expanding Universe: Majorana-Oppenheimer Formalism, Exact Solutions in non-Static Coordinates
O. V. Veko, N. D. Vlasii, E. M. Ovsiyuk, V. M. Red'kov, Yu. A. Sitenko

Tetrad-based generalized complex formalism by Majorana-Oppenheimer is applied to treat an electromagnetic field on expanding de Sitter Universe in non-static spherically-symmetric coordinates. With the help of the Wigner D-functions, we separate angular dependence in the complex vector field E_j(t, r)+iB_j(t, r) from (t, r)-dependence. The separation parameter arising here instead of frequency ω in Minkowski space-time is quantized, non-static geometry of the de Sitter model leads to definite dependence of electromagnetic modes on time variable. Relation of 3-vector complex approach to 10-dimensional Duffin-Kemmer-Petiau formalism is considered. On this base, the electromagnetic waves of magnetic and electric type have been constructed in both approaches. In Duffin-Kemmer-Petiau approach, there are constructed gradient-type solutions in Lorentz gauge.

Key words: de Sitter Universe, electromagnetic field, Majorana-Oppenheimer formalism, non-static coordinates, electric and magnetic waves

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