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advanced_tools:bianchi_identities [2019/01/16 14:24] 129.13.36.189 [Concrete] |
advanced_tools:bianchi_identities [2019/01/16 14:34] jakobadmin [Abstract] |
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- | 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." ([[https://link.springer.com/article/10.1007%2FBF01882731|Source]]) |
- | </note> | + | |
<tabbox Why is it interesting?> | <tabbox Why is it interesting?> | ||
<blockquote> | <blockquote> |