Almost Everywhere Flatness of a 3-Space with a Loop-Based Wormhole

dc.creatorTurakulov, Z. Ya.
dc.date2005-01-11
dc.date.accessioned2026-07-07T05:15:59Z
dc.date.available2026-07-07T05:15:59Z
dc.descriptionA particular Riemannian metric which originally has been obtained for a well-known coordinate system in the Euclidean 3-space, is shown to specify, in fact, a manifold with boundary. There are two ways to make the manifold complete. One is to identify two halves of the boundary that turns the manifold into Euclidean 3-space as it was done originally. Another is to identify boundaries of two copies of this manifold, that yields a complete manifold which consists of two copies of Euclidean 3-space connected through a round disk. In general relativity this kind of connection is called `loop-based wormhole'. The straightforward calculation of curvature from the metric specified yields an erroneous result, due which the curvature is zero, that is impossible because a manifold with this structure cannot be flat. This paradox is resolved in full correspondence with the generally-accepted definitions.
dc.descriptionLaTeX, 6 pages
dc.identifierhttps://arxiv.org/abs/math/0501169
dc.identifierhttp://arxiv.org/abs/math/0501169
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/73822
dc.subjectDifferential Geometry
dc.subject53C25; 53A99
dc.titleAlmost Everywhere Flatness of a 3-Space with a Loop-Based Wormhole
dc.typetext

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