Christoffel symbols

  1. I am learning about christoffel symbols and there is a pretty standard representation of christoffel symbols as a linear combination of products of the metric tensor and the metric tensors derivative. However when this is derived it is always done in a hoakey manner. Something along the lines of .... do these permutations add this subtract that and walllaaa. I am trying to make a more physically intuitive proof based off the covariant derivative of the metric tensor being equal to zero. Has anyone seen this proof somewhere i havent got it to work out and i am looking go help.
     
  2. jcsd
  3. nicksauce

    nicksauce 1,275
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    Check out chapter 3 of Wald's GR book.
     
  4. Fredrik

    Fredrik 10,298
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    I think the best place to read about connections is "Riemannian manifolds: an introduction to curvature", by John Lee. But I don't remember how he did this particular thing.
     
  5. HallsofIvy

    HallsofIvy 40,504
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    The ordinary derivative of a tensor is NOT a tensor. In order to make it one, the "covariant derivative", you have to subtract off the Christoffel symbols- or, to put it another way, the Chrisoffel symbols are the covariant derivative minus the ordinary derivative.
     
  6. dx

    dx 2,010
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    Yes, you can find it in MTW exercise 8.15. It has an outline solution too.
     
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