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advanced_tools:bianchi_identities [2018/05/03 11:58]
jakobadmin [Intuitive]
advanced_tools:bianchi_identities [2019/01/16 14:35] (current)
jakobadmin [Abstract]
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   ​   ​
 <tabbox Concrete> ​ <tabbox Concrete> ​
 +For an extremely illuminating discussion see
 +
 +  * [[https://​link.springer.com/​article/​10.1007%2FBF01882731|The Boundary of a Boundary Principle - a unified approach]] by Arkady Kheyfets.
 +
 +In addition, good discussion can be found in
 +
   * See chapter 15 in "​Gravitation"​ by Misner Thorne and Wheeler and also   * See chapter 15 in "​Gravitation"​ by Misner Thorne and Wheeler and also
   * page 253 in Gauge fields, knots, and gravity by J. Baez   * page 253 in Gauge fields, knots, and gravity by J. Baez
  
-  +----
-<tabbox Abstract> ​+
  
-<note tip> +Bianchi identities express ​the fact that the boundary ​of a boundary is always zeroMathematically this follows by applying Stoke'​s theorem twice. This is discussed explicitly in the book No-Nonsense Electrodynamics by Schwichtenberg
-The motto in this section is: //the higher ​the level of abstraction,​ the better//. +
-</​note>​+
  
 + 
 +<tabbox Abstract> ​
 +In general relativity, the Bianchi identity ​
 +$$ \nabla R = \nabla \nabla \theta =0  $$
 +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]])
 <tabbox Why is it interesting?> ​ <tabbox Why is it interesting?> ​
 <​blockquote>​ <​blockquote>​
advanced_tools/bianchi_identities.1525341536.txt.gz · Last modified: 2018/05/03 09:58 (external edit) · Currently locked by: 172.71.158.95,216.244.66.248