Lagrangian evolution of the Weyl tensor

Edmund Bertschinger, A. J. S. Hamilton
1994 Astrophysical Journal  
We derive the evolution equations for the electric and magnetic parts of the Weyl tensor for cold dust from both general relativity and Newtonian gravity. In a locally inertial frame at rest in the fluid frame, the Newtonian equations agree with those of general relativity. We give explicit expressions for the electric and magnetic parts of the Weyl tensor in the Newtonian limit. In general, the magnetic part does not vanish, implying that the Lagrangian evolution of the fluid is not purely local.
more » ... d is not purely local.
doi:10.1086/174787 fatcat:qgyadvlcfnawdhrtr6e2l67zva