Wrong results in Variation of action

[SHIVAM SINGH KUSHWAH]

Can someone please guide where things went wrong?

Einstein tensor Eab is vanising which is wrong.

Einstein tensor Eab in terms of A_{a} is vanising which is wrong.

Maxwell Equation in terms of A_{a}, is giving error.

Why it is so?

Regards

Shivam

[Juan Margalef]

Hi Shivam,

The short answer to your first two questions is that you need to use something additional, like xPert. I recommend you to take a look at the website https://contrib.xact.es/. In particular, you can find some examples here: https://github.com/xAct-contrib/examples

As for the third question, notice that the error is already telling you the problem: "Found indices with the same name -b". If you do a bit of debugging, you will find that the term Aterm^2 is the one causing the problem because it is equivalent to

F[-a, -b]F[a, b]F[-a, -b]F[a, b]

which has repeated indices. The quickest solution is to wrap the definition with Scalar: Aterm=Scalar[F[a,b]F[-a,-b]].