🎬how to calculate divergence in a curved coordinate system

In a curved coordinate system, the naive divergence, which is a simple calculation of partial derivatives that becomes physically meaningless as the grid warps, must be precisely corrected by the Christoffel term, a dynamic mathematical factor that accounts for the coordinate system's curvature, in order to produce the covariant divergence, which is the true and constant measure of the vector field's expansion regardless of the grid's deformation.

Contraction of the Christoffel Symbols and the Metric Determinant | Proof and Derivationviadean on Notion