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Action of Einstein equations

  1. Jul 27, 2008 #1
    I have a problem with deriving Einstein equations :

    [tex]\epsilon_{IJKL}(e^{I} \wedge R^{JK} + \lambda e^{I} \wedge e^{J} \wedge e^{K}) = 0[/tex]

    [tex]de^{I} + \omega^{I}_{J} \wedge e^{J} = 0[/tex]

    From the action :

    [tex]S[e , \omega] = \frac{1}{16 \pi G} \int \epsilon_{IJKL} (e^{I} \wedge e^{J} \wedge R^{KL} + e^{I} \wedge e^{J} \wedge e^{K} \wedge e^{L})[/tex]

    Using Euler-Lagrange equations, for example for the first one I found:

    [tex]\epsilon_{IJKL}(e^{I} \wedge R^{JK} + 2 \lambda e^{I} \wedge e^{J} \wedge e^{K}) = 0[/tex]

    I know that my problem is surely simple :confused: but I'm back to calculus after a long time of absence :cry: thx2
  2. jcsd
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