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What do I do with these christoffel symbols?

  1. Oct 22, 2011 #1
    Hey guys I'm a bit new to GR and stuck on this question? :/. So we are given that:

    d2xi/dλ2+[itex]\Gamma[/itex]ijk dxi/dλ dxj/dλ = 0

    and asked to show that d/dλ(gijdxi/dλdxj/dλ) = 0

    So I expanded using the product rule to get:

    [itex]\Gamma[/itex]ijkd2xi/dλ2 dxj/dλ +[itex]\Gamma[/itex]ijk dxi/dλd2 xj/dλ2

    Then rearranged the first equation to get:

    d2xi/dλ2 = - [itex]\Gamma[/itex]ijkdxi/dλ dxj/dλ

    and substituted for the second order differential equations. That's where I get stuck as I don't know how to get rid of the christoffel symbols. I read somewhere that they have a high degree of symmetry - so maybe I can change the dummy indices to get a symmetric form and they cancel? Very confused - any help would be appreciated.
     
  2. jcsd
  3. Oct 22, 2011 #2

    Matterwave

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    Science Advisor
    Gold Member

    I believe you are missing a term d(gij)/dλ*...?

    I guess I don't follow exactly your "expand" term. If you skipped a lot of steps, I can't do them in my head haha.

    There's something wrong with the indices though, you have two of the same indices "upstairs" (implied sum or not?), which almost never happens.
     
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