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Einstein action with tetrads

  1. Jun 3, 2015 #1
    I would like to write the HIlbert-Einstein action using tetrad formalism.
    I have seen in a paper that the lagrangian is the contraction between a levi civita tensor, against two veilbeins and a two form curvature.
    The problem is that i can' t prove that this is the same as the scalar curvature moltiplied by the determinant of the metric.
    Could you help me? I am sure of the result, but i can' prove it
  2. jcsd
  3. Jun 3, 2015 #2


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    See section 3.2: "Covariant Loop Quantum Gravity", by Rovelli and Vidotto, published by Cambridge University Press.
    Last edited by a moderator: Jun 5, 2015
  4. Jun 3, 2015 #3
    Thanks you really much :)
    I had a launch with Carlo Rovelli and Francesca Vidotto, they were really nice: it s a surprise to see the solution in their book
    Last edited by a moderator: Jun 5, 2015
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