get einstein tensor for a metric with undetermined functions

james madison

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Dec 20, 2022, 1:11:12 AM12/20/22

to xAct Tensor Computer Algebra

Hi,
I was wondering if it is possible to get the einstein tensor for a metric that has some undetermined function/s (say f[x1]).

I tried doing it with some template notebook by replacing terms of a given metric with f[r] and it did not work.

TIA

TB

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Dec 20, 2022, 1:15:12 AM12/20/22

to xAct Tensor Computer Algebra

Hi!

You have to tell the system that f is a scalar function first with DefScalarFunction[f].

Also remember that r is a tensor field with valence 0, so you have to give it an empty list of indices, i.e. you have to write f[r[]].

Regards
Thomas

Jose

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Dec 20, 2022, 10:06:13 AM12/20/22

to xAct Tensor Computer Algebra

Hi,

See also examples in sections 3.5 and 3.6 of the notebook xAct/Documentation/English/xCobaDoc.nb, particularly subsections 3.5.2 and 3.5.3 using metrics with all components being general functions.

Cheers,

Jose.

james madison

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Dec 20, 2022, 5:53:27 PM12/20/22

to xAct Tensor Computer Algebra

Thank you. That makes sense.

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