2011/09/01 by Е. М. Ovsiyuk, Ovsiyuk, E. M., В. М. Редьков +1
Mathematics · Physics and Astronomy · #35 #Algebraic and Geometric Analysis #Classical Physics (physics.class-ph) #FOS: Physical sciences #G.1 #Mathematical Physics (math-ph) #Quantum and Classical Electrodynamics #Relativity and Gravitational Theory
paper · pdf · doi:10.48550/arxiv.1109.0126
openalex publication_date 2011/09/01 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/28
Lobachewsky geometry simulates a medium with special constitutive relations. The situation is specified in quasi-cartesian coordinates (x,y,z). Exact solutions of the Maxwell equations in complex 3-vector form, extended to curved space models within the tetrad formalism, have been found in Lobachevsky space. The problem reduces to a second order differential equation which can be associated with an 1-dimensional Schrodinger problem for a particle in external potential field U(z) = U0 e2z. In quantum mechanics, curved geometry acts as an effective potential barrier with reflection coefficient R=1; in electrodynamic context results similar to quantum-mechanical ones arise: the Lobachevsky geometry simulates a medium that effectively acts as an ideal mirror. Penetration of the electromagnetic field into the effective medium, depends on the parameters of an electromagnetic wave, ω, k12 + k22, and the curvature radius ρ.