http://en.wikipedia.org/wiki/Four-force(adsbygoogle = window.adsbygoogle || []).push({});

At the bottom of that page, the author provides the generalization of four force in general relativity, where the partial derivative is replaced with the covariant derivative.

However if you notice on the second term in the third equality, there is a four vector summed on mu with the gamma symbols, is that there to select the 0th component of the gamma symbol? Since in a MCRF frame, the spatial components of U are all 0.

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# Weird version of covariant derivative on wikipedia

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