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Christoffel Symbols?

  • Thread starter atomqwerty
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  • #1
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My question is just,

How can I determinate the Christoffel Symbols?

I know that they're given by

http://img263.imageshack.us/i/17f2df132717bfc32dc2ce3.png/" [Broken]

but, what does this mean? The subscripts I mean.

thank you very much!! :)
 
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Answers and Replies

  • #2
tiny-tim
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hi atomqwerty! :smile:
what does this mean? The subscripts I mean.
each index has to take all the values 0 1 2 3 (or 1 2 3 4) :wink:

(and then sum over all repeated indices … the Einstein summation convention)

and yes, it does take a long time :rolleyes: … but it helps that most of the derivatives are zero tongue2)
 
  • #3
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hi atomqwerty! :smile:


each index has to take all the values 0 1 2 3 (or 1 2 3 4) :wink:
I see, but, what is for example g12 for a given g?

thanks!
 
  • #4
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It is [tex]\frac{g_{mk}}{x_{l}}= \frac{\partial}{\partial x_{l}} \frac{\partial g_{m}}{\partial x_{k}}[/tex]?

thanks
 
  • #5
tiny-tim
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I see, but, what is for example g12 for a given g?

thanks!
g is the metric …

g12 is the coefficient of dx1dx2 :wink:

(and g11 is the coefficient of dx12 etc)
 
  • #6
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g is the metric …

g12 is the coefficient of dx1dx2 :wink:

(and g11 is the coefficient of dx12 etc)
With [tex]dx_{1}dx_{2}[/tex] you mean [tex]dx_{1}\otimes dx_{2}[/tex], right?
 
  • #7
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The whole expression it's a sum, right? So for a metrics in R2, there will be... 24 different addends (12 for each k)?? :O

EDIT: Automessage- It's not a sum, they are Symbols!!! My fault :S
 
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  • #8
tiny-tim
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With [tex]dx_{1}dx_{2}[/tex] you mean [tex]dx_{1}\otimes dx_{2}[/tex], right?
ooh, that's rather technical, we don't normally bother with that in physics :redface:
The whole expression it's a sum, right? So for a metrics in R2, there will be... 24 different addends (12 for each k)?? :O

EDIT: Automessage- It's not a sum, they are Symbols!!! My fault :S
not following you :confused:
 
  • #9
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ooh, that's rather technical, we don't normally bother with that in physics :redface:
It's for differential Geometry ;)

Thank you, it's been very helpfull! :approve:
 

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