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More simply a tensor algebra question, but in General relativity I have the following when I calculate $\Gamma_{00}^\lambda$:-

$$ \Gamma_{00}^\lambda = \frac{1}{2}g^{\nu\lambda}\left( \frac{\partial g_{0\nu}}{\partial x^0} + \frac{\partial g_{0\nu}}{\partial x^0} - \frac{\partial g_{00}}{\partial x^\nu} \right) = -\frac{1}{2}g^{\nu\lambda} \frac{\partial g_{00}}{\partial x^\nu} $$

Why are the $\frac{\partial g_{0\nu}}{\partial x^0}$ terms zero?

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What is the metric for which you are computing the connection coefficients? – joshphysics Apr 26 '13 at 20:33
Hi rgvcorley: Echoing @joshphysics' comment: Without further context, this question seems incomplete. – Qmechanic Apr 26 '13 at 20:58
@Qmechanic it's ok John M below was able to read between the lines - clearly if what I have written is true then the metric must be time invariant – rgvcorley Apr 26 '13 at 21:10
up vote 1 down vote accepted

The elements of this particular metric tensor do not depend on time. $dx^j$ and $dt$ are treated as constants when you take the time derivative.

You should also have $\Gamma^{\lambda}_{00} = -\frac{1}{2} g^{\nu \lambda} \frac{\partial g_{00}}{\partial x^\nu}$.

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Of course! Thankyou! – rgvcorley Apr 26 '13 at 20:35

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