Metric perturbation in xAct

[Safinaz Salem]

Hello,

I start to learn xAct. I noticed that xAct set a default perturbation to the metric by the above code, then for instance for first order perturbation: 

It gives: 

And  I understand that g[-a, -b] is a diagonal metric : (-1,1,1,1). However, I want to make another perturbation for a new metric: met= a(t)^2 Exp[y] (-1,1,1,1)

And the perturbation is given by:

Can this be fulfilled by xAct?  Here the perturbation for each metric component 

𝑔00,𝑔0𝑖, and 𝑔𝑖𝑗 is different. And I don’t get how this can be done in xAct.  the final expression I want to perturb is:

Thanks! 

[Obinna Umeh]

Hi Safinaz

 xPand which is built on the xAct framework can do it. 

Download and install xPand https://github.com/Obinna/xPand/tree/master and then check out this example https://github.com/Obinna/xPand/tree/master/Examples

Cheers

Obinna

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[Safinaz Salem]

Hello Obinna

Thanks for your answer

I downloded xPand with xAct, there are many examples in the package, but it sill not clear for me how to define a new metric pertirbation.

I tried to use a Mathematica code with no exra packages and define the pertubered metric, then substite by in  the ( G\alpha\beta) eqution, but the code’s output  is too large and non linearized. 

Cheers

Safinaz 

[Obinna Umeh]

Hi Safinaz

You should have a look at the xPand documentation, there are examples there on how to choose a gauge if that is your problem. It would help to read this paper https://arxiv.org/abs/1302.6174 on how xPand works.  Note that it is xPert that does metric perturbations.

xPand does an N+1 decomposition of perturbed metric variables on a homogenous background. If you do not like this approach, xCoba will be another option you can try.

If there is a specific issue you encounter, you should send a tiny notebook example of it.

All the best. 

Obinna

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