[tex] \nabla_a[(-g)^{\frac{1}{2}}T^a] = T^a\nabla_a[(-g)^{\frac{1}{2}}]+(-g)^{\frac{1}{2}}\nabla_aT^a[/tex](adsbygoogle = window.adsbygoogle || []).push({});

I just realized that I don't quite understand how a tensor density behaves when multiplied by a vector. I'm trying to find some clues in D'Inverno's book but I'm getting more confused.

Thanks in advance :)

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# Is this valid?

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