2,963 research outputs found
Self-similar Bianchi models: I. Class A models
We present a study of Bianchi class A tilted cosmological models admitting a
proper homothetic vector field together with the restrictions, both at the
geometrical and dynamical level, imposed by the existence of the simply
transitive similarity group. The general solution of the symmetry equations and
the form of the homothetic vector field are given in terms of a set of
arbitrary integration constants. We apply the geometrical results for tilted
perfect fluids sources and give the general Bianchi II self-similar solution
and the form of the similarity vector field. In addition we show that
self-similar perfect fluid Bianchi VII models and irrotational Bianchi
VI models do not exist.Comment: 14 pages, Latex; to appear in Classical and Quantum Gravit
G_2 cosmological models separable in non-comoving coordinates
We study new separable orthogonally transitive abelian G_2 on S_2 models with
two mutually orthogonal integrable Killing vector fields. For this purpose we
consider separability of the metric functions in a coordinate system in which
the velocity vector field of the perfect fluid does not take its canonical
form, providing thereby solutions which are non-separable in comoving
coordinates in general. Some interesting general features concerning this class
of solutions are given. We provide a full classification for these models and
present several families of explicit solutions with their properties.Comment: latex, 26 pages, accepted for publication in Class. Quantum Gra
Asymptotic self-similarity breaking at late times in cosmology
We study the late time evolution of a class of exact anisotropic cosmological
solutions of Einstein's equations, namely spatially homogeneous cosmologies of
Bianchi type VII with a perfect fluid source. We show that, in contrast to
models of Bianchi type VII which are asymptotically self-similar at late
times, Bianchi VII models undergo a complicated type of self-similarity
breaking. This symmetry breaking affects the late time isotropization that
occurs in these models in a significant way: if the equation of state parameter
satisfies the models isotropize as regards the shear
but not as regards the Weyl curvature. Indeed these models exhibit a new
dynamical feature that we refer to as Weyl curvature dominance: the Weyl
curvature dominates the dynamics at late times. By viewing the evolution from a
dynamical systems perspective we show that, despite the special nature of the
class of models under consideration, this behaviour has implications for more
general models.Comment: 29 page
Global dynamics of the mixmaster model
The asymptotic behaviour of vacuum Bianchi models of class A near the initial
singularity is studied, in an effort to confirm the standard picture arising
from heuristic and numerical approaches by mathematical proofs. It is shown
that for solutions of types other than VIII and IX the singularity is velocity
dominated and that the Kretschmann scalar is unbounded there, except in the
explicitly known cases where the spacetime can be smoothly extended through a
Cauchy horizon. For types VIII and IX it is shown that there are at most two
possibilities for the evolution. When the first possibility is realized, and if
the spacetime is not one of the explicitly known solutions which can be
smoothly extended through a Cauchy horizon, then there are infinitely many
oscillations near the singularity and the Kretschmann scalar is unbounded
there. The second possibility remains mysterious and it is left open whether it
ever occurs. It is also shown that any finite sequence of distinct points
generated by iterating the Belinskii-Khalatnikov-Lifschitz mapping can be
realized approximately by a solution of the vacuum Einstein equations of
Bianchi type IX.Comment: 16 page
A new proof of the Bianchi type IX attractor theorem
We consider the dynamics towards the initial singularity of Bianchi type IX
vacuum and orthogonal perfect fluid models with a linear equation of state. The
`Bianchi type IX attractor theorem' states that the past asymptotic behavior of
generic type IX solutions is governed by Bianchi type I and II vacuum states
(Mixmaster attractor). We give a comparatively short and self-contained new
proof of this theorem. The proof we give is interesting in itself, but more
importantly it illustrates and emphasizes that type IX is special, and to some
extent misleading when one considers the broader context of generic models
without symmetries.Comment: 26 pages, 5 figure
The Asymptotic Behaviour of Tilted Bianchi type VI Universes
We study the asymptotic behaviour of the Bianchi type VI universes with a
tilted -law perfect fluid. The late-time attractors are found for the
full 7-dimensional state space and for several interesting invariant subspaces.
In particular, it is found that for the particular value of the equation of
state parameter, , there exists a bifurcation line which signals a
transition of stability between a non-tilted equilibrium point to an extremely
tilted equilibrium point. The initial singular regime is also discussed and we
argue that the initial behaviour is chaotic for .Comment: 22 pages, 4 figures, to appear in CQ
Cylindrically symmetric dust spacetime
We present an explicit exact solution of Einstein's equations for an
inhomogeneous dust universe with cylindrical symmetry. The spacetime is
extremely simple but nonetheless it has new surprising features. The universe
is ``closed'' in the sense that the dust expands from a big-bang singularity
but recollapses to a big-crunch singularity. In fact, both singularities are
connected so that the whole spacetime is ``enclosed'' within a single
singularity of general character. The big-bang is not simultaneous for the
dust, and in fact the age of the universe as measured by the dust particles
depends on the spatial position, an effect due to the inhomogeneity, and their
total lifetime has no non-zero lower limit. Part of the big-crunch singularity
is naked. The metric depends on a parameter and contains flat spacetime as a
non-singular particular case. For appropriate values of the parameter the
spacetime is a small perturbation of Minkowski spacetime. This seems to
indicate that flat spacetime may be unstable against some global {\it
non-vacuum} perturbations.Comment: LaTeX, 6 pages, 1 figure. Uses epsfig package. Submitted to Classical
and Quantum Gravit
The flatness problem and
By way of a complete integration of the Friedmann equations, in terms of
observables, it is shown that for the cosmological constant there
exist non-flat FLRW models for which the total density parameter
remains throughout the entire history of the universe. Further, it is
shown that in a precise quantitative sense these models are not finely tuned.
When observations are brought to bear on the theory, and in particular the WMAP
observations, they confirm that we live in just such a universe. The conclusion
holds when the classical notion of is extended to dark energy.Comment: Final form to appear in Physical Review Letters. Further information
at http://grtensor.org/Robertson
Design and performance of a multicentre, randomized controlled trial of teleconsulting.
We have designed and performed a multicentre, randomized controlled trial of teleconsulting. The trial investigated the effectiveness and cost implications in rural and inner-city settings of using videoconferencing as an alternative to general practitioner referral to a hospital specialist. The participating general practitioners referred a total of 3170 patients who satisfied the entry criteria. Of these, 1040 (33%) failed to provide consent or otherwise refused to participate in the trial. Of the patients recruited to the trial, a total of 1902 (91%) completed and returned the baseline questionnaire. Although the trial was successful in recruiting sufficient patients and in obtaining high questionnaire response rates, the findings will require careful interpretation to take account of the limits which the protocol placed on the ability of general practitioners to select patients for referral
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