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Results tagged with tensor-calculus
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user 102456
Tensor calculus (tensor analysis) is a systematic extension of vector calculus to multivector and tensor fields in a form that is independent of the choice of coordinates on the relevant manifold, but which accounts for respective sub-spaces, their symmetries, and their connections.
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Multiple skew brackets in tensor summation, e.g. $U_{[ab]}V^{[ab]}$
I'm wondering what does $U_{[ab]}V^{[ab]}$ or $U_{[ab]}V^{(ab)}$ usually mean? I thought the double brackets meant to apply the $\text{sgn}(\pi)$ twice so $$U_{[ab]}V^{[ab]}=\frac{1}{2}\sum_{a,b}\left …
- 175
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How to derive $\nabla_{\mu} T^{\mu\nu}=\frac{1}{\sqrt {-g}}\partial_{\mu}(\sqrt{-g}\,T^{\mu\...
This $$\nabla_{\mu} T^{\mu\nu}=\frac{1}{\sqrt {-g}}\partial_{\mu}(\sqrt{-g}\,T^{\mu\nu})\tag{3.39}$$ is from a textbook on general relativity on black hole Vaidya metric, where only non-zero term of s …
- 175