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Newtonian Evolution of the Weyl Tensor

In an interesting recent paper on the growth of inhomogeneity through the effect of gravity, Bertschinger & Hamilton derive equations for the electric and magnetic parts of the Weyl tensor for cold dust in both general relativity and Newtonian theory. Their conclusion is that in both general relativity and Newtonian theory, in general, the magnetic part of the Weyl tensor does not vanish, implying that the Lagrangian evolution of the fluid is not local. We show here that the “Newtonian” theory they discuss is in fact not Newtonian theory per se but rather a plausible relativistic generalization of Newtonian theory. Newtonian cosmology itself is highly nonlocal irrespective of the behavior of the magnetic part of the Weyl tensor; in this respect, the Bertschinger-Hamilton generalization is a better theory.