AutomaticRules for traceless tensor

[Albin Nilsson]

I am trying to define a new tensor with the same symmetries as the Weyl tensor, i.e. RiemannSymmetric + tracelessness. 

Looking at the documentation for AutomaticRules, it seems like I have to make a rule for each index, for example:

AutomaticRule[T, MakeRule[{T[a,-a,-c,-d],0}]]

and so on. 

Is there a way of doing this in a more compact way?

Thanks in advance

[Leo Stein]

Hi Albin,

I took a stab at this idea back in 2013 with an xTension called TraceFree, which is available in this repo: https://github.com/xAct-contrib/TraceFree .

If you install this xTension and then load it, then at the time when you define a tensor, you can write something along the lines of:

> DefTensor[S[a, b, c], M4, Symmetric[{a, b, c}], TraceFree -> {a, b, c}]

or, for your scenario,

> DefTensor[T[a, b, c, d], M4, RiemannSymmetric[{a, b, c, d}], TraceFree -> {a, b, c, d}]

However, I haven't been using this xTension, so the code may be out of date. But give it a try and see if it still does what it's supposed to do.

Best

Leo

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[Albin Nilsson]

Hi Leo, 

it works great, thanks for the help!