Anti-Newtonian universes do not exist

In a paper by Maartens, Lesame and Ellis (Class. Quant. Grav. 15, 1005) it was shown that irrotational dust solutions with vanishing electric part of the Weyl tensor are subject to severe integrability conditions and it was conjectured that the only such solutions are FLRW spacetimes. In their analysis the possibility of a cosmological constant Lambda was omitted. The conjecture is proved, irrespective as to whether Lambda is zero or not, and qualitative differences with the case of vanishing magnetic Weyl curvature are pointed out.Comment: 16 page

A Petrov type I and generically asymmetric rotating dust family

The general line element corresponding to the family of algebraically general, gravito-electric, expanding, rotating dust models with one functionally independent zero-order Riemann invariant is constructed. The isometry group is at most one-dimensional but generically trivial. It is shown that the asymmetric solutions with constant ratio of energy density and vorticity amplitude provide first examples of Petrov type I space-times for which the Karlhede classification requires the computation of the third covariant derivative of the Riemann tensor.Comment: 7 pages, irrotational limit case added, several minor errors correcte

Three-dimensional spacetimes of maximal order

We show that the equivalence problem for three-dimensional Lorentzian manifolds requires at most the fifth covariant derivative of the curvature tensor. We prove that this bound is sharp by exhibiting a class of 3D Lorentzian manifolds which realize this bound. The analysis is based on a three-dimensional analogue of the Newman-Pen-rose formalism, and spinorial classification of the three-dimensional Ricci tensor.Comment: final revision

Note on aligned Petrov type D purely magnetic perfect fluids

We recently showed (Class. Quantum Grav.\ 23, 3353; gr-qc/0602091) that aligned Petrov type D purely magnetic perfect fluids are necessarily locally rotationally symmetric (LRS) and hence are all explicitly known. We provide here a more transparent proof.Comment: 8 pages, no figures. Note on gr-qc/060209

An exhaustive classification of aligned Petrov type D purely magnetic perfect fluids

We prove that aligned Petrov type D purely magnetic perfect fluids are necessarily locally rotationally symmetric and hence are all explicitly known.Comment: 7 pages typos corrected and references adde

Maximally inhomogeneous G\"{o}del-Farnsworth-Kerr generalizations

It is pointed out that physically meaningful aligned Petrov type D perfect fluid space-times with constant zero-order Riemann invariants are either the homogeneous solutions found by G\"{o}del (isotropic case) and Farnsworth and Kerr (anisotropic case), or new inhomogeneous generalizations of these with non-constant rotation. The construction of the line element and the local geometric properties for the latter are presented.Comment: 4 pages, conference proceeding of Spanish Relativity Meeting (ERE 2009, Bilbao