Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Christoffel symbols

  1. Mar 29, 2010 #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. Mar 29, 2010 #2

    nicksauce

    User Avatar
    Science Advisor
    Homework Helper

    Check out chapter 3 of Wald's GR book.
     
  4. Mar 29, 2010 #3

    Fredrik

    User Avatar
    Staff Emeritus
    Science Advisor
    Gold Member

    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. Mar 30, 2010 #4

    HallsofIvy

    User Avatar
    Science Advisor

    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. Mar 30, 2010 #5

    dx

    User Avatar
    Homework Helper
    Gold Member

    Yes, you can find it in MTW exercise 8.15. It has an outline solution too.
     
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook