Re: [xAct] Perturbating the inverse metric using xPert (elementary)

[Leo Stein]

Hi Sashwat,

The convention for xPert is to include the factor of 1/n! in perturbation series. This is stated explicitly close to the beginning of the accompanying journal article (https://arxiv.org/abs/0807.0824), but I see that it's easy to miss this if you're just looking at xPertDoc.nb. In xPertDoc.nb you will find documentation of the command Perturbed[expr, order] which gives you the series up to your desired order, including the factors of epsilon and 1/n!. I would recommend using Perturbed[] rather than writing out the sum yourself. Attached is an example notebook showing the correct matrix inverse property (and here is a screenshot of the contents of that notebook).

Best

Leo

On Thu, Aug 1, 2024 at 4:49 PM Sashwat Tanay <sashwa...@gmail.com> wrote:

Hi everybody,

I am trying to perturbatively expand the inverse metric using xPert. xPert gives me an answer. When I try to verify the answer, the result is not as expected.

I expect that perturbation-expanded versions (up to 2nd order) of the metric and the inverse metric when multiplied together should give Kronecker delta up to 2nd order. But I get a remnant term h^{1ba} h^{1}_{ca}.

What did I do wrong?

Regards,

Sashwat Tanay

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[Sashwat Tanay]

I see, it's clear now. Thanks a lot!

Maybe the documentation notebook can be improved somewhat stating clearly what exactly "Perturbation" produces. 

On a different note, ChatGPT is not good at producing xAct codes. Do you think making a lot of xAct code publicly available can fix that? Jose M. Garcia does not seem very interested in this proposition in his email reply to me.

Regards,

Sashwat Tanay

Postdoctoral fellow

Laboratoire Univers et Theories (LUTH)

CNRS/Paris Observatory/Paris Cité University

5 place Jules Janssen, 92190 Meudon, France

Building 18, Evry Schatzman, Office 233

sashwa...@obspm.fr

https://sashwattanay.github.io/site