🎬how the divergence field emerges from the antisymmetric tensor

For an antisymmetric rank-(2,0) tensor built from a scalar amplitude t ( $T^{12}=t, T^{21}=-t$ ), the divergence is the 90°-rotated gradient, $∇_a T^{ab} = (−∂_y t, ∂_x t)$. The demo shows that the antisymmetric tensor encodes a circulation-like field whose divergence is orthogonal to ∇t and has the same local magnitude structure, illustrating the geometric relation between antisymmetry and rotation.

Divergence of an Antisymmetric Tensor in Terms of the Metric Determinant | Proof and Derivationviadean on Notion