## Divergence

The divergence of a Vector Field is given by

 (1)

Define
 (2)

Then in arbitrary orthogonal Curvilinear Coordinates,

 (3)

If , then the field is said to be a Divergenceless Field. For divergence in individual coordinate systems, see Curvilinear Coordinates.
 (4)

The divergence of a Tensor is
 (5)

where is the Covariant Derivative and is the Comma Derivative. Expanding the terms gives
 (6)

Arfken, G. Divergence, .'' §1.7 in Mathematical Methods for Physicists, 3rd ed. Orlando, FL: Academic Press, pp. 37-42, 1985.