advanced_tools:bianchi_identities
| Both sides previous revision Previous revision Next revision | Previous revision | ||
|
advanced_tools:bianchi_identities [2019/01/16 14:24] 129.13.36.189 [Concrete] |
advanced_tools:bianchi_identities [2019/01/16 14:35] (current) jakobadmin [Abstract] |
||
|---|---|---|---|
| Line 28: | Line 28: | ||
| ---- | ---- | ||
| - | Bianchi identities express the fact that the boundary of a boundary is always zero. Mathematically this follows by applying Stoke's theorem twice. | + | Bianchi identities express the fact that the boundary of a boundary is always zero. Mathematically this follows by applying Stoke's theorem twice. This is discussed explicitly in the book No-Nonsense Electrodynamics by Schwichtenberg |
| <tabbox Abstract> | <tabbox Abstract> | ||
| - | + | In general relativity, the Bianchi identity | |
| - | <note tip> | + | $$ \nabla R = \nabla \nabla \theta =0 $$ |
| - | The motto in this section is: //the higher the level of abstraction, the better//. | + | roughly says "that the sum over a closed two-dimensional surface of rotations induced by Riemannian curvature is equal to zero. [...] Geometrically this means that the density of the moment of rotation induced by Riemannian curvature is equal to zero automatically." ([[https://link.springer.com/article/10.1007%2FBF01882731|Source]]) |
| - | </note> | + | |
| <tabbox Why is it interesting?> | <tabbox Why is it interesting?> | ||
| <blockquote> | <blockquote> | ||
advanced_tools/bianchi_identities.1547645097.txt.gz · Last modified: 2019/01/16 13:24 (external edit)
Page Tools
Except where otherwise noted, content on this wiki is licensed under the following license: CC Attribution-Share Alike 4.0 International
