Affine connection contraction

1. Jun 15, 2013

coqui82

Hi everyone!

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 }}

2. Jun 15, 2013

Bill_K

(You can embed LaTeX code directly in your post by wrapping it with TEX or ITEX.)

Yes, you're correct, the reason the last two terms drop out is that they are antisymmetric in μ and ρ, and we're multiplying by gμρ which is symmetric.

3. Jun 15, 2013

WannabeNewton

Does Weinberg actually call the Christoffel symbols an affine connection ?

4. Jun 15, 2013

coqui82

Thanks a lot Bill! Much more clear now!
And yes, Weinberg uses both terms, although affine connection is a more general one.

5. Jun 17, 2013

George Jones

Staff Emeritus
What is wrong with this?