Is the following true?(adsbygoogle = window.adsbygoogle || []).push({});

[tex]\Gamma_{\mu \nu \alpha}+\Gamma_{\nu \mu \alpha}=-2\Gamma_{\alpha \mu \nu}[/tex]

where:

[tex]\Gamma_{\alpha \mu \nu}=g_{\alpha \sigma}\Gamma^{\sigma}_{~\mu \nu}[/tex]

I ask because, while bored in a philosophy lecture, I decided to try to derive the geodesic equation by extremizing ∫g_{μν}u^{μ}u^{ν}dλ, where u^{μ}= dx^{μ}/dλ.

I was able to arrive at the following, where a_{μ}=du_{μ}/dλ:

[tex]2a_\alpha = (\Gamma_{\mu \nu \alpha}+\Gamma_{\nu \mu \alpha})u^\mu u^\nu [/tex]

So, am I on the right track or did I make an error somewhere?

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# Christoffel Symbol Question

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