Help obtaining correct equations of motion

[Alejandro Aguilar]

Hi everyone,

I have been having some difficulty understanding how to obtain the correct equations of motions using XPert, as I am writing the same Lagrangian in different forms (I contract the Levi-Civita antisymmetric tensor to other tensor) and I am obtaining different sets of Einstein Field equations, even though they should be the same. Im attaching a notebook with a toy model to illustrate my problem. 
If someone please explain what is going on and how do I make sure that the field equations Im obtaining are correct I would greatly appreciate it.

Cheers,

Alejandro

[Juan Margalef]

Hi Alejandro.

It is hard to check your notebook since it is not selfcontained, try to add all the definitions to make sure it can be run by others. I have made some quick trials and I get, as expected, the same EOM for L1a, L1b and L1c. Likewise, I got the same for L2a, L2b and L2c (but different, as expected as well, from L1a). Analogously for L3. (Important! the three set should lead to different EOM since some have inverse metrics hidden when you raise/lower indices). If you had a working minimal example, we could take a detailed look to see why you get different results when you shouldn't. 

Best,

Juan