Physics Forums

Physics Forums (http://www.physicsforums.com/index.php)
-   Special & General Relativity (http://www.physicsforums.com/forumdisplay.php?f=70)
-   -   Christoffel symbols (http://www.physicsforums.com/showthread.php?t=390703)

zwoodrow Mar29-10 08:31 PM

Christoffel symbols
 
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.

nicksauce Mar29-10 08:54 PM

Re: Christoffel symbols
 
Check out chapter 3 of Wald's GR book.

Fredrik Mar29-10 09:27 PM

Re: Christoffel symbols
 
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.

HallsofIvy Mar30-10 06:38 AM

Re: Christoffel symbols
 
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.

dx Mar30-10 09:48 AM

Re: Christoffel symbols
 
Quote:

Quote by zwoodrow (Post 2645961)
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.

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


All times are GMT -5. The time now is 01:25 AM.

Powered by vBulletin Copyright ©2000 - 2014, Jelsoft Enterprises Ltd.
© 2014 Physics Forums