Mass current (${\mathbf{j}}_m=\rho \mathbf{v}$)

The flux of mass carried by a continuum moving with velocity $\mathbf{v}$. In the nonrelativistic limit, ${\partial }_t\rho +\nabla \cdot {\mathbf{j}}_m=0$ is local mass conservation. A stationary mass current can produce a stationary gravitomagnetic field without emitting gravitational radiation.