795 research outputs found
On tilted perfect fluid Bianchi type VI self-similar models
We show that the tilted perfect fluid Bianchi VI family of self-similar
models found by Rosquist and Jantzen [K. Rosquist and R. T. Jantzen, \emph{%
Exact power law solutions of the Einstein equations}, 1985 Phys. Lett.
\textbf{107}A 29-32] is the most general class of tilted self-similar models
but the state parameter lies in the interval .
The model has a four dimensional stable manifold indicating the possibility
that it may be future attractor, at least for the subclass of tilted Bianchi
VI models satisfying in which it belongs. In addition
the angle of tilt is asymptotically significant at late times suggesting that
for the above subclasses of models the tilt is asymptotically extreme.Comment: Latex, 7 pages, no figures; (v2) some clarification comments are
added in the discussion and one reference; (v3) minor corrections in
equations (1), (3) and (19
Geometric equations of state in Friedmann-Lema\^{i}tre universes admitting matter and Ricci Collineations
As a rule in General Relativity the spacetime metric fixes the Einstein
tensor and through the Field Equations (FE) the energy-momentum tensor. However
one cannot write the FE explicitly until a class of observers has been
considered. Every class of observers defines a decomposition of the
energy-momentum tensor in terms of the dynamical variables energy density
(), the isotropic pressure (), the heat flux and the traceless
anisotropic pressure tensor . The solution of the FE requires
additional assumptions among the dynamical variables known with the generic
name equations of state. These imply that the properties of the matter for a
given class of observers depends not only on the energy-momentum tensor but on
extra a priori assumptions which are relevant to that particular class of
observers. This makes difficult the comparison of the Physics observed by
different classes of observers for the {\it same} spacetime metric. One way to
overcome this unsatisfactory situation is to define the extra condition
required among the dynamical variables by a geometric condition, which will be
based on the metric and not to the observers. Among the possible and multiple
conditions one could use the consideration of collineations. We examine this
possibility for the Friedmann-Lema\^{i}tre-Robertson-Walker models admitting
matter and Ricci collineations and determine the equations of state for the
comoving observers. We find linear and non-linear equations of state, which
lead to solutions satisfying the energy conditions, therefore describing
physically viable cosmological models.Comment: 14 pages, Latex; to appear in General Relativity and Gravitatio
Uniqueness of Petrov type D spatially inhomogeneous irrotational silent models
The consistency of the constraint with the evolution equations for spatially
inhomogeneous and irrotational silent (SIIS) models of Petrov type I, demands
that the former are preserved along the timelike congruence represented by the
velocity of the dust fluid, leading to \emph{new} non-trivial constraints. This
fact has been used to conjecture that the resulting models correspond to the
spatially homogeneous (SH) models of Bianchi type I, at least for the case
where the cosmological constant vanish. By exploiting the full set of the
constraint equations as expressed in the 1+3 covariant formalism and using
elements from the theory of the spacelike congruences, we provide a direct and
simple proof of this conjecture for vacuum and dust fluid models, which shows
that the Szekeres family of solutions represents the most general class of SIIS
models. The suggested procedure also shows that, the uniqueness of the SIIS of
the Petrov type D is not, in general, affected by the presence of a non-zero
pressure fluid. Therefore, in order to allow a broader class of Petrov type I
solutions apart from the SH models of Bianchi type I, one should consider more
general ``silent'' configurations by relaxing the vanishing of the vorticity
and the magnetic part of the Weyl tensor but maintaining their ``silence''
properties i.e. the vanishing of the curls of and the pressure
.Comment: Latex, 19 pages, no figures;(v2) some clarification remarks and an
appendix are added; (v3) minor changes to match published versio
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