1,935 research outputs found
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
Bodily relations and reciprocity in the art of Sonia Khurana
This article explores the significance of the ‘somatic’ and ‘ontological turn’ in locating the radical politics articulated in the contemporary performance, installation, video and digital art practices of New Delhi-based artist, Sonia Khurana (b. 1968). Since the late 1990s Khurana has fashioned a range of artworks that require new sorts of reciprocal and embodied relations with their viewers. While this line of art practice suggests the need for a primarily philosophical mode of inquiry into an art of the body, such affective relations need to be historicised also in relation to a discursive field of ‘difference’ and public expectations about the artist’s ethnic, gendered and national identity. Thus, this intimate, visceral and emotional field of inter- and intra-action is a novel contribution to recent transdisciplinary perspectives on the gendered, social and sentient body, that in turn prompts a wider debate on the ethics of cultural commentary and art historiography
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
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
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
An almost isotropic cosmic microwave temperature does not imply an almost isotropic universe
In this letter we will show that, contrary to what is widely believed, an
almost isotropic cosmic microwave background (CMB) temperature does not imply
that the universe is ``close to a Friedmann-Lemaitre universe''. There are two
important manifestations of anisotropy in the geometry of the universe, (i) the
anisotropy in the overall expansion, and (ii) the intrinsic anisotropy of the
gravitational field, described by the Weyl curvature tensor, although the
former usually receives more attention than the latter in the astrophysical
literature. Here we consider a class of spatially homogeneous models for which
the anisotropy of the CMB temperature is within the current observational
limits but whose Weyl curvature is not negligible, i.e. these models are not
close to isotropy even though the CMB temperature is almost isotropic.Comment: 5 pages (AASTeX, aaspp4.sty), submitted to Astrophysical Journal
Letter
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
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
- …