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Question tensors

  1. Nov 15, 2009 #1
    if i have a tensor[tex]T^{uv}[/tex]...i need to calculate the covariant derivate [tex]T^u_{v;a}[/tex]

    The logical thing is to do [tex]T^u_v[/tex] and next to calculate [tex]T^u_{v;a}[/tex]

    is also correct to first calculate[tex]T^{uv}_{;a}[/tex] and next [tex]T^u_{v;a}=T^{ui}_{;a}g_{iv}[/tex]???
     
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  3. Nov 15, 2009 #2

    Ben Niehoff

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    Yes, provided we choose a connection which is "compatible" with the metric. There is a unique such connection, and it is the one we choose to use in GR.
     
  4. Nov 15, 2009 #3
    What Ben Niehoff means by metric compatibility is that you must be careful in taking the derrivative of the metric.

    Usually, in general relativity, the connection is chosen such that

    [tex]\nabla_{\sigma} \ g_{\mu\nu} = 0 \ .[/itex]

    It simplifies things.
     
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