Defining a constant tensor in xAct

[Shubham]

Hi all,

How can I define a constant tensor (with any number and kind of indices) in xAct? I can't use DefConstantSymbol because it is only for a scalar.

Thanks!

[Jose]

Hi,

I think this question needs more context.

I don't think there is a general concept of constant tensor that can be implemented in xTensor. Take a tensor whose components are constants in some coordinate system. If you change to another coordinate system then the new components will not be constant in general. So how can we define a geometric notion of "being constant" ?

If you have a tensor T and you know that some covariant derivative cd gives 0 on that tensor then write

cd[_][_T] ^:= 0

If you are working with xTensor and you are assuming you have a single coordinate system and your tensor is constant in that system then you can use PD instead of cd.

If you are working with xCoba and you have defined one or more coordinate systems then use the corresponding derivatives of those charts instead of cd. Depending on how you have setup your metric field, you may also need to specify that some partial derivatives of some scalar functions are zero.

Cheers,

Jose.