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Keywords = Riemann–Weyl–Finsler spaces

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16 pages, 294 KiB  
Article
Six-Dimensional Manifold with Symmetric Signature in a Unified Theory of Gravity and Electromagnetism
by Nikolay Popov and Ivan Matveev
Symmetry 2022, 14(6), 1163; https://doi.org/10.3390/sym14061163 - 5 Jun 2022
Cited by 6 | Viewed by 1739
Abstract
A six dimensional manifold of symmetric signature (3,3) is proposed as a space structure for building combined theory of gravity and electromagnetism. Special metric tensor is proposed, yielding the space which combines the properties of Riemann, Weyl and Finsler [...] Read more.
A six dimensional manifold of symmetric signature (3,3) is proposed as a space structure for building combined theory of gravity and electromagnetism. Special metric tensor is proposed, yielding the space which combines the properties of Riemann, Weyl and Finsler spaces. Geodesic line equations are constructed where coefficients can be divided into depending on the metric tensor (relating to the gravitational interaction) and depending on the vector field (relating to the electromagnetic interaction). If there is no gravity, the geodesics turn into the equations of charge motion in the electromagnetic field. Furthermore, symmetric six-dimensional electrodynamics can be reduced to traditional four-dimensional Maxwell system, where two additional time dimensions are compactified. A purely geometrical interpretation of the concept of electromagnetic field and point electric charge is proposed. Full article
(This article belongs to the Special Issue Foundations of Continuum Mechanics and Mathematical Physics)
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