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I have some problems with indices in general relativity. I am now working with the classic textbook by S. Weinberg and in eq. (4.7.4) we find

http://latex.codecogs.com/gif.latex...partial g_{\rho \mu }}{\partial x^{\lambda }}

The question is: where does the last equality come from?

I think that it could come from the comparison between this expression and the same one interchanging μ and ρ. In so doing you would get the same expression except for the last two partial derivatives that would change their sign. Now if you consider (I am not sure if this is right) that http://latex.codecogs.com/gif.latex?\Gamma^{\mu}_{\mu \lambda }=\Gamma ^{\rho }_{\rho \lambda } then it comes straightforwardly that http://latex.codecogs.com/gif.latex...partial g_{\mu \lambda }}{\partial x^{\rho }}

Thanks in advance!

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# Affine connection contraction

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