Almost Everywhere Flatness of a 3-Space with a Loop-Based Wormhole
| dc.creator | Turakulov, Z. Ya. | |
| dc.date | 2005-01-11 | |
| dc.date.accessioned | 2026-07-07T05:15:59Z | |
| dc.date.available | 2026-07-07T05:15:59Z | |
| dc.description | A 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.description | LaTeX, 6 pages | |
| dc.identifier | https://arxiv.org/abs/math/0501169 | |
| dc.identifier | http://arxiv.org/abs/math/0501169 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/73822 | |
| dc.subject | Differential Geometry | |
| dc.subject | 53C25; 53A99 | |
| dc.title | Almost Everywhere Flatness of a 3-Space with a Loop-Based Wormhole | |
| dc.type | text |