NEWTONIAN-LIKE AND ANTI-NEWTONIAN UNIVERSES

In an irrotational dust universe the locally free gravitational field is covariantly described by the gravito-electric and gravito-magnetic tensors E-ab and H-ab. In Newtonian theory, H-ab = 0 and E-ab is the t idal tensor. Newtonian-like dust universes in general relativity (i.e. with H-ab = 0, often called 'silent') have been shown to be inconsist ent in general and unlikely to extend beyond the known spatially homog eneous or Szekeres examples. Furthermore, they are subject to a linear ization instability. Here we show that 'anti-Newtonian' universes, i.e . with purely gravito-magnetic field, so that E-ab = 0 not equal H-ab, are also subject to severe integrability conditions. Thus these model s are inconsistent in general. We show also that there are no anti-New tonian spacetimes that are linearized perturbations of Robertson-Walke r universes. The only E-ab = 0 not equal H-ab solution known to us is not a dust solution, and we show that it is kinematically Godel-like b ut dynamically unphysical.