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Metric connection

  1. Jul 11, 2014 #1
    Dear all,

    In my journey through learning General relativity. I have stumbled upon this problem. I have to calculate the geodesic equation for R[itex]^{3}[/itex] in cylindrical polars. I am not sure how to use the metric connection. The indices confuse me. I would appreciate it if someone could shade some light on it. Every time I try to calculate it I get zero, sometimes due to the first metric tensor and sometime the terms in the parentheses are zeros.

    [itex]\Gamma_{bc}^{a}=\frac{1}{2}g^{ad}(\partial_{b}g_{dc}+\partial_{c}g_{db}-\partial_{d}g_{bc})[/itex]

    As I understand it, the index d is the dummy index and runs from 1 to 3 in this case, right? What about b and c? how do I use them?

    Thanks in advance
     
  2. jcsd
  3. Jul 11, 2014 #2
    Yes and a, b and c can be 1, 2 or 3 giving 27 gamma's.

    You have to calculate all the gamma's, but a lot of them are equals or vanish.

    What did you find for the metric in these coordinates?
     
  4. Jul 11, 2014 #3
    I actually got it now :smile:

    Thanks bloby
     
  5. Jul 11, 2014 #4
    Ok, you're welcome.
     
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