- #1
astros
- 22
- 0
Hi,
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 but I'm back to calculus after a long time of absence thx2
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 but I'm back to calculus after a long time of absence thx2