LAGRANGIAN EVOLUTION OF THE WEYL TENSOR

We derive the evolution equations for the electric and magnetic parts of the Weyl tenser for cold dust from both general relativity and Newt onian gravity. In a locally inertial frame at rest in the fluid frame, the Newtonian equations agree with those of general relativity. We gi ve explicit expressions for the electric and magnetic parts of the Wey l tenser in the Newtonian limit. In general, the magnetic part does no t vanish, implying that the Lagrangian evolution of the fluid is not p urely local.