Majorana-Oppenheimer Approach to Maxwell Electrodynamics. Part III. Electromagnetic Spherical Waves in Spaces of Constant Curvature

Complex formalism of Riemann-Silberstein-Majorana-Oppenheimer in Maxwell electrodynamics extended to the case of arbitrary pseudo-Riemannian space-time applied to solve the Maxwell equations are solved exactly on the background of simplest static cosmological models, spaces of constant curvature of Riemann and Lobachevsky parameterized by spherical coordinates. Separation of variables is realized in the basis of Schrodinger-Pauli type, description of angular dependence in electromagnetic complex 3-vectors is given in terms of Wigner D-functions. In the case of compact Riemann model a discrete frequency spectrum for electromagnetic modes depending on the curvature radius of space and three discrete parameters is found. In the case of hyperbolic Lobachevsky model no discrete spectrum for frequencies of electromagnetic modes arises.