Evaluating xTensor expressions for a given metric using xCoba

[Quim Llorens Giralt]

Hi everyone,

I have some long abstract expressions that I have computed using xTensor.
Now, I would like to evaluate them using xCoba in some particular metrics (like AdS, Schw, etc) without having to rewrite them again.

Is there a function that evaluates an abstract expression given a particular metric in xCoba? I'm sure there is, but I haven't easily found it and I'm getting confused because sometimes xAct doesn't know which metric to use (either the abstract or the particular one).

I attach an easy example.

Thanks in advance!
Quim

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[jose xact.es]

Hi,

Yes, this functionality has been requested a number of times. The thing to do is to write a list of rules replacing the abstract objects by the respective component tensors, which can be done by hand to be specific about which tensors are needed. But I understand it can be automated. So I've written a simple function doing this at the end of your notebook. If this is not enough, send another example with something that doesn't work.

Cheers,

Jose.

---

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Subject: [xAct] Evaluating xTensor expressions for a given metric using xCoba

 

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[Quim Llorens Giralt]

Thank you very much!
This is exactly what I was looking for.

Quim

[徐涌群]

Hi

Jose did a great job!

And I throuth I have a naive edition of this, about ansatz compont evaluation. It was mentioned a lot in this group.

I was try to get equation 5 in the paper:[2009.00512v2] Tensor Perturbations and Thick Branes in Higher-dimensional $f(R)$ Gravity (arxiv.org)

 

My code in attached below. Hope it may help 

Best regard

Yongqun Xu 

[Jose]

Hi,

I reattach your notebook with the computation I think you want.

I must say that I generally don't look at computations that involve comparing with articles, because it usually takes much time, but this case was relatively clear.

Cheers,

Jose.

On Wednesday, October 6, 2021 at 3:26:24 PM UTC-5 phy...@gmail.com wrote:

Hi

Jose really did a great job! He has posed several reply about ansatz compont evaluation. I have learned a lot form them.

And now I have a easier edition of this. I was trying to get equation 5 in the paper:[2009.00512v2] Tensor Perturbations and Thick Branes in Higher-dimensional $f(R)$ Gravity (arxiv.org)

 

My code in attached below. Hope it may help 

Best regards

Yongqun Xu

在2021年10月5日星期二 UTC+8 上午12:29:20<qllo...@icc.ub.edu> 写道：

[Geová Maciel de Alencar Filho]

Hi, can the same be done with a tensor? I have an abstract tensor, and now I wanna it in some particular basis, with spherical symmetry and  components depending on "r".

thanks

[Bing-Nan Liu]

Hi,

I encounter a weird problem when using Jose's function. The "ReplaceMetric[ ]" doesn't work when evaluating the "g[-\[Mu], -\[Nu]]*CD[a][phi[]]*CD[-b][CD[b][CD[-a][phi[]]]]" term. However, when I divide the term into two terms: "g[-\[Mu], -\[Nu]]" and "CD[a][phi[]]*CD[-b][CD[b][CD[-a][phi[]]]]", then the code works. The stress tensor I get has almost 50 terms, all the other terms are fine except this one, which is the "Subscript[SE, 6.2]", in[43] in my code. I sincerely ask for anyone's help.

I attach my whole .nb.

Thanks in advance!

Bingnan

[Jose]

Hi,

This is a case in which performing the replacement of the scalar field phi[] earlier helps quite a lot in the computation, because they become much simpler. Redefine:

ReplaceMetric[expr_, rule : Rule[ametric_, cmetric_]] := FromBasisExpand@Expand[ SeparateMetric[ametric][expr] /. MetricReplacements[rule] /. phi[] -> \[Xi][rr[]] ]

where I've just added the phi[] rule at the end, to be inside the Expand call. Then things should work better, and you will not need to have that rule at every step of the computation.

Cheers,

Jose.

[Bing-Nan Liu]

Hi Jose,

Thank you so much for that short and elegant optimization! The code works very well now.

Thank you again for your time!

Cheers,

Bingnan