Alternate form of geodesic equation

  • Thread starter Alexrey
  • Start date
  • #1
35
0

Homework Statement


We're asked to show that the geodesic equation [tex]\frac{du^{a}}{dt} +\Gamma^{a}_{bc}u^{b}u^{c}=0[/tex] can be written in the form [tex]\frac{du_{a}}{dt}=\frac{1}{2}(\partial_{a}g_{cd})u^{c}u^{d}[/tex]




Homework Equations


[tex]\Gamma^{a}_{bc}=\frac{1}{2}g^{ad}(\partial_{b}g_{dc}+\partial_{c}g_{bd}-\partial_{d}g_{bc})[/tex]



The Attempt at a Solution


I tried contracting the geodesic equation with [tex]g_{ab}[/tex] but came out with some Kronecker deltas which stumped me a bit.
 

Answers and Replies

  • #2
196
22
It can't be true in general. (pun!)

Is there some kind of simplifying assumption or approximation that makes 2 of the terms go away? Perhaps you're studying the Newtonian limit?
 

Related Threads on Alternate form of geodesic equation

  • Last Post
Replies
3
Views
1K
  • Last Post
Replies
5
Views
3K
  • Last Post
Replies
0
Views
3K
  • Last Post
Replies
2
Views
1K
Replies
1
Views
1K
Replies
2
Views
6K
Replies
1
Views
2K
Replies
3
Views
2K
  • Last Post
Replies
1
Views
889
Top