Electric currents in multiply connected spaces
Electric currents are considered within the framework of electromagnetism (electric fields solving Maxwell's equations) in a space-time of the form \({\mathbb{R}}\times V^ 3\). Theorem 1: No current flux through a closed 2- sided surface whose area is bounded in time, can be maintained for an infinite time. Theorem 2: Let space-time be a conformally static universe, and let C be a spatial wire loop that has zero intersection number with every closed 2-sided surface in the spatial section V. Then a current in C can be maintained for the lifetime of the universe. - Thus it depends on the topology of space whether one can maintain a current in any wire loop.
scientific article; zbMATH DE number 4100123