|Oct22-11, 09:16 AM||#1|
What do I do with these christoffel symbols?!
Hey guys I'm a bit new to GR and stuck on this question? :/. So we are given that:
d[SUP]2[SUP]xi/dλ2+[itex]\Gamma[/itex]ijk dxi/dλ dxj/dλ = 0
and asked to show that d/dλ(gijdxi/dλdxj/dλ) = 0
So I expanded using the product rule to get:
[itex]\Gamma[/itex]ijkd2xi/dλ2 dxj/dλ +[itex]\Gamma[/itex]ijk dxi/dλd2 xj/dλ2
Then rearranged the first equation to get:
d[SUP]2[SUP]xi/dλ2 = - [itex]\Gamma[/itex]ijkdxi/dλ dxj/dλ
and substituted for the second order differential equations. That's where I get stuck as I don't know how to get rid of the christoffel symbols. I read somewhere that they have a high degree of symmetry - so maybe I can change the dummy indices to get a symmetric form and they cancel? Very confused - any help would be appreciated.
|Oct22-11, 04:32 PM||#2|
I believe you are missing a term d(gij)/dλ*...?
I guess I don't follow exactly your "expand" term. If you skipped a lot of steps, I can't do them in my head haha.
There's something wrong with the indices though, you have two of the same indices "upstairs" (implied sum or not?), which almost never happens.
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