How to use CTensor for the Maxwell stress tensor F?

I have used the CTensor to compute an equation of motion. Everything is ok but the stress tensor F. How can I rewrite this tensor using CTensor. The needed definitions are as follows:

DefManifold[M, 6, {\[Alpha], \[Beta], \[Sigma], \[Delta], \[Iota], \
\[Mu], \[Omicron], \[FinalSigma], \[Tau], \[Upsilon], \[Chi], \
\[Omega], \[Nu], \[Rho], \[Gamma]}]

DefChart[\[ScriptCapitalB], M, {0, 1, 2, 3, 4, 5}, {t[],
r[], \[Eta]1[], \[Zeta]1[], \[Eta]2[], \[Zeta]2[]},
ChartColor -> Blue]

MakeRule[{F[-\[Alpha], -\[Beta]],
CD[-\[Alpha]]@A[-\[Beta]] - CD[-\[Beta]]@A[-\[Alpha]]}]

and A(r) is

A = {h[r[]], 0, 0, 2 h[r[]] m \[Eta]1[], 0, 2 h[r[]] m \[Eta]2[]}.

• Have you defined a metric? I'm pretty sure that xAct & xCoba need one to do coordinate calculations involving CD. Also, I believe that you'll need to invoke DefScalarFunction[h] to let xCoba know that h is a scalar function of your coordinates, and it's probably good practice to invoke DefConstantSymbol[m] as well (assuming it is in fact a constant.) Jul 16 '19 at 14:41