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Electric currents in multiply connected spaces. (English) Zbl 0672.53058

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.
Reviewer: D.Erle

MSC:

53C80 Applications of global differential geometry to the sciences
53C50 Global differential geometry of Lorentz manifolds, manifolds with indefinite metrics
55N45 Products and intersections in homology and cohomology
78A25 Electromagnetic theory (general)
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References:

[1] Frankel, T. (1979).Gravitational Curvature, Freeman, San Francisco. · Zbl 0427.53009
[2] Misner, C., Thorne, K., and Wheeler, J. (1973).Gravitation, Freeman, San Francisco.
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