Newtonian Evolution of the Weyl Tensor

Abstract

In an interesting recent paper on the growth of inhomogeneity through the effect of gravity [1], Bertschinger and Hamilton derive equations for the electric and magnetic parts of the Weyl tensor for cold dust for both General Relativity and Newtonian theory. Their conclusion is that both in General Relativity and in 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 discussed by them is in fact not Newtonian theory {\it per se}, but rather a plausible relativistic generalisation of Newtonian theory. Newtonian cosmology itself is highly non-local irrespective of the behaviour of the magnetic part of the Weyl tensor; in this respect the Bertschinger-Hamilton generalisation is a better theory.