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Divergence of mixed II-order tensors

  1. Jun 27, 2008 #1
    Dear friends,
    How is the divergence in curvilinear coordinates of a second order mixed tensor defined? I mean, shall I contract the covariant or the contravariant index?? And for both cases which is the physical meaning?

    [tex]\nabla_i N^i_j[/tex] or [tex]\nabla_j N^i_j [/tex]?

    Thanks a lot,
  2. jcsd
  3. Jun 28, 2008 #2


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    Science Advisor

    You should always contract lower indices with upper indices in the first place. I think you're confused because the energy momentum tensor T is symmetric, so it doesn't mind with which index you contract.

    The physical meaning of the divergence depends on what the tensor T represents; it depends on what the [tex]T^{\alpha\beta}[/tex] means for fixed [tex]\alpha[/tex] or fixed [tex]\beta[/tex]. You could put other conserved quantities in some tensor T; the divergence of one of the indices means then covariant conservation of that quantity.
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