# Action of Einstein equations

1. Jul 27, 2008

### astros

Hi,
I have a problem with deriving Einstein equations :

$$\epsilon_{IJKL}(e^{I} \wedge R^{JK} + \lambda e^{I} \wedge e^{J} \wedge e^{K}) = 0$$

$$de^{I} + \omega^{I}_{J} \wedge e^{J} = 0$$

From the action :

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

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

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

I know that my problem is surely simple but I'm back to calculus after a long time of absence thx2