Dear Wolfram team:
I try to calculate :
$T_{ab} = g_{ab} F_{gd} F^{gd} - F_a^g F_{bg}$,
where
$F_{ab} = \partial_a A_b - \partial_b A_a$,
So I define $F_{ab}$ by:
s[a_, b_] := D[v[b], a] - D[v[a], b]
But how to define $F^{ab}$ and $F_a^b$ ?
$g_{ab}$ is given by:
metric = DiagonalMatrix[{-1, 1, 1, 1}];
m[a_, b_] := metric[[a, b]];
