582 research outputs found
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
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
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
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