Four-divergence (${\partial }_{\mu }{V}^{\mu }$)

The four-divergence of a four-vector field is the Lorentz scalar contraction ${\partial }_{\mu }{V}^{\mu }$. With $x^{\mu }=(ct,\mathbf{x})$, it equals $c^{-1}{\partial }_t{V}^0+\nabla \cdot \mathbf{V}$. The four-current has zero four-divergence, expressing local charge conservation.