OK, my computer program (GRTensor II) says that(adsbygoogle = window.adsbygoogle || []).push({});

[tex]\Gamma_{abc}[/tex] is symmetric in the first two indices. Which leads to the equation

[tex] \Gamma_{abc} = \frac{1}{2} ( \frac{\partial g_{bc}}{\partial a}+ \frac{\partial g_{ac}}{\partial b} - \frac{\partial g_{ab}}{\partial c} ) [/tex]

And that's exactly what it calculates.

Unfortunately, my textbook seems to insist that the minus sign belongs on the first term above, not the last - but there would be no way for the symbol to be symmetric in the first two indices if that were true. Another text seems to agree with the first.

Right now I'm tempted towards beliving my computer program over the textooks. This gives the result that

[tex]\Gamma_{xtt} = \frac{1}{2} \frac{\partial g_{tt}}{\partial x}[/tex]

which is necessary to get the very simple result that the "forces" on a stationary body are just the gradient of g_{tt}in nearly flat space-time (the Newtonian limit) which Pete mentions.

Does anyone know for sure where the minus sign belongs?

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# Embarassingly simple question - Christoffel symbols

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