I have some fairly basic (hopefully) questions about tensor equations. Hopefully someone here can help out.(adsbygoogle = window.adsbygoogle || []).push({});

Let us say I have a tensor equation, (I will use this as the example for discussion: [tex]A^{u} = b C^{uv}D_{v}[/tex]).

If this is true in one coordinate system, it will be true in all of them correct?

Now if I know the components of A,C,D in one frame (as well as the metric in this frame), then I can find the components of A,C,D in any other frame by transforming them, correct?

Can I get the metric in this new frame by transforming the metric like a normal tensor as well (it does not seem to work in general... maybe I am making mistakes)?

How do nonlinear transformations work? (For instance if I wanted to find A,C,D in an accelerated frame.) Since the transformation tensor just gives a linear transformation ... it seems to suggest that I need the metric to no longer be a constant in the frame!? Or does it work some other way?

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# Tensor equations / nonlinear transformations

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