# Christoffel symbols

1. Mar 29, 2010

### zwoodrow

I am learning about christoffel symbols and there is a pretty standard representation of christoffel symbols as a linear combination of products of the metric tensor and the metric tensors derivative. However when this is derived it is always done in a hoakey manner. Something along the lines of .... do these permutations add this subtract that and walllaaa. I am trying to make a more physically intuitive proof based off the covariant derivative of the metric tensor being equal to zero. Has anyone seen this proof somewhere i havent got it to work out and i am looking go help.

2. Mar 29, 2010

### nicksauce

Check out chapter 3 of Wald's GR book.

3. Mar 29, 2010

### Fredrik

Staff Emeritus
I think the best place to read about connections is "Riemannian manifolds: an introduction to curvature", by John Lee. But I don't remember how he did this particular thing.

4. Mar 30, 2010

### HallsofIvy

The ordinary derivative of a tensor is NOT a tensor. In order to make it one, the "covariant derivative", you have to subtract off the Christoffel symbols- or, to put it another way, the Chrisoffel symbols are the covariant derivative minus the ordinary derivative.

5. Mar 30, 2010

### dx

Yes, you can find it in MTW exercise 8.15. It has an outline solution too.