The question is simple, what is the result of the following multiplication of traces by the metric?


It seems confusing to me because I don't see clearly if it's equal to zero or not.

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    $\begingroup$ The formula is malformed, in relativity the sum convention is to sum over an index occurring twice once as co- and once as contravariant index. (I guess the indices on the $g$ should be down?) $\endgroup$ – Sebastian Riese May 10 '18 at 18:00
  • $\begingroup$ @SebastianRiese that's not the point actually, I edited the question. The problem is how to compute the product between Levi-Civita tensor and the metric tensors. $\endgroup$ – Enri May 10 '18 at 18:54
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    $\begingroup$ The Wikipedia page for the Levi-Civita has some contraction identities. $\endgroup$ – knzhou May 10 '18 at 18:55

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