- #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)

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)

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