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Covariant derivative

  1. Jul 4, 2007 #1
    just a quick query, I know that,

    [itex] \nabla_0 A_{\alpha}= \partial_0 A_{\alpha} - \Gamma^{\beta}_{0 \alpha} A_{\beta} [/itex]

    But what does
    [itex] \nabla^0 A_{\alpha} [/itex] equal?
     
  2. jcsd
  3. Jul 4, 2007 #2
    Since [itex]\nabla^0A_\alpha = g^{0\beta}\nabla_\beta A_\alpha[/itex] you have

    [tex]\nabla^0A_\alpha = g^{0\beta}\partial_\beta A_\alpha - g^{0\beta}\Gamma^{\gamma}_{\phantom{\gamma}\alpha\beta}A_\gamma[/tex]
     
  4. Jul 13, 2007 #3
    You're welcome.
     
  5. Jul 13, 2007 #4

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    Don't take it personally, it's rare to get thanked for help here.
     
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