Re: [xAct] Varying an action with respect to the metric

[Leo Stein]

Dear Fardous Merzoug,

There are some examples of how to use VarD in the file xAct/Documentation/English/xTensorDoc.nb that's included in the distribution. However when varying with respect to the metric, you have to be careful about implicit dependence. This is made simpler by using xPert to find the 1st order perturbation — which handles all the implicit dependencies — and then varying with VarD. There are two examples in the repo https://github.com/xAct-contrib/examples , named Lagrangian-variation-xPert-VarD.nb and ActionVariation_Metric_Fields.nb . Also, the package xTras introduced the function VarL which automates this operation.

Best

Leo

On Sat, Jan 18, 2025 at 10:10 AM Fardous Merzoug <fardous...@g.ens-kouba.dz> wrote:

I want to Varying an action with respect to the metric to obtain the  equations of motion, Is there any way to do that in Mathematica without using xAct? Can mathematica do that?and also is there any xAct documentation for  that or  Example codes and references would be more helpful. Thank you!

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