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Homework Help: Covariant derivate problem (christoffel symbols)

  1. Jul 9, 2014 #1
    1. The problem statement, all variables and given/known data

    I need to calculate [tex] \square A_\mu + R_{\mu \nu} A^\nu [/tex] if [tex] \square = \nabla_\alpha \nabla^\alpha [/tex], and is the covariant derivate

    SEE THIS PDF arXiv:0807.2528v1 i wanna get the equation (5) from (3)

    2. Relevant equations

    [tex] A^{i}_{{;}{\alpha}} = \frac{{\partial}{A^{i}}}{{\partial}{x^{\alpha}}} + \Gamma^{i}_{{j}{\alpha}} A^{j} [/tex]

    Lool arXiv:hep-th/0504052v2 for the conections and christoffel symbols o ricci tensor components

    3. The attempt at a solution

    for example The 00 component for Ruv is

    [tex] R_{\mu \nu} = -3(\dot{H}+H^2) [/tex]

    see the links for more compoents
  2. jcsd
  3. Jul 10, 2014 #2
    Do you see why only one equation remains?
    How ##\square ## is expressed with low index nabla's only?
    Do you know the expression for ##A_{{\alpha}{;}{\beta}}## ?

    (I use latin indices for space components and greek indices for space-time components)

    note: if you past an url it becomes clickable, for inline latex wrap it with ##.


    eq (8)
    Last edited: Jul 10, 2014
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