Finding a Christoffel symbol

  • Thread starter jordy1113
  • Start date
  • #1
jordy1113
12
3
Homework Statement:
Find Christoffel symbol
Relevant Equations:
$$
\Gamma^l_{ki} = \frac{1}{2} g^{lj} (\partial_k g_{ij} + \partial_i g_{jk} - \partial_j g_{ki})
$$
\begin{eqnarray}
g_{00}(x,t)=1\\
g_{0i}(x,t)=0\\
g_{ij}(x,t)=a^{2}(t)[\delta_{ij}+h_{ij}(x,t)]\\
\end{eqnarray}
I was not given a formal teaching on christoffel symbols and how to find them so I just need some help.
I'm trying to find the cristoffel symbol:
\begin{equation}
\Gamma^{i}_{00}
\end{equation}
I set my equation up as:
\begin{equation}
\Gamma^i_{00} = \frac{1}{2} g^{ij} (\partial_0 g_{0j} + \partial_0 g_{0j} - \partial_j g_{00})
\end{equation}
Am I correct in getting that this christoffel symbol is equal to zero? If not what am I doing wrong? Many thanks in advance (sorry I am still trying to figure out the latex on the forum)
 
Last edited:

Answers and Replies

  • #2
anuttarasammyak
Gold Member
1,939
1,012
From (5) you seem to be right. Why do not you calculate general jk components not only 00 ?
If not all components are zero, you would have some confidence.
 
  • #3
haushofer
Science Advisor
Insights Author
2,731
1,200
You're right, but what kind of metric is this?
 
  • #4
jordy1113
12
3
You're right, but what kind of metric is this?
cosmological synchronous gauge according to Dodelson and Schmidt
 
  • #5
jordy1113
12
3
From (5) you seem to be right. Why do not you calculate general jk components not only 00 ?
If not all components are zero, you would have some confidence.
thanks, I calculated some of the other christoffel symbols already and my professor checked them, we just forgot to do this one so I needed some reassurance I was doing it correctly
 

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