When we derive equation of motion by variation of the action, we use rules of ordinary differentiation and integration. So only ordinary derivatives can appear in the equation. Now in general relativity we are supposed to replace all those ordinary derivatives by covariant derivatives. Is that how one rigorously get equations valid in general relativity?(adsbygoogle = window.adsbygoogle || []).push({});

Second, suppose there is a term like \del_m(1/ \sqrt{1-g^{ab}T,aT,b}). Will I have have to replace the ordinary derivatives in the denominator also in this case?

I have these doubts. Can anybody clear these? Also I am not sure if this is the best place to ask such questions, just trying since I am trying to learn things alone. Are there other websites where one can ask such questions and get help? Thanks.

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# Use of covariant derivative in general relativity.

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