1,910 research outputs found
Curvature blow up in Bianchi VIII and IX vacuum spacetimes
The maximal globally hyperbolic development of non-Taub-NUT Bianchi IX vacuum
initial data and of non-NUT Bianchi VIII vacuum initial data is C2
inextendible. Furthermore, a curvature invariant is unbounded in the incomplete
directions of inextendible causal geodesics.Comment: 20 pages, no figures. Submitted to Classical and Quantum Gravit
Asymptotic silence-breaking singularities
We discuss three complementary aspects of scalar curvature singularities:
asymptotic causal properties, asymptotic Ricci and Weyl curvature, and
asymptotic spatial properties. We divide scalar curvature singularities into
two classes: so-called asymptotically silent singularities and non-generic
singularities that break asymptotic silence. The emphasis in this paper is on
the latter class which have not been previously discussed. We illustrate the
above aspects and concepts by describing the singularities of a number of
representative explicit perfect fluid solutions.Comment: 25 pages, 6 figure
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
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
Conformal regularization of Einstein's field equations
To study asymptotic structures, we regularize Einstein's field equations by
means of conformal transformations. The conformal factor is chosen so that it
carries a dimensional scale that captures crucial asymptotic features. By
choosing a conformal orthonormal frame we obtain a coupled system of
differential equations for a set of dimensionless variables, associated with
the conformal dimensionless metric, where the variables describe ratios with
respect to the chosen asymptotic scale structure. As examples, we describe some
explicit choices of conformal factors and coordinates appropriate for the
situation of a timelike congruence approaching a singularity. One choice is
shown to just slightly modify the so-called Hubble-normalized approach, and one
leads to dimensionless first order symmetric hyperbolic equations. We also
discuss differences and similarities with other conformal approaches in the
literature, as regards, e.g., isotropic singularities.Comment: New title plus corrections and text added. To appear in CQ
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
New explicit spike solution -- non-local component of the generalized Mixmaster attractor
By applying a standard solution-generating transformation to an arbitrary
vacuum Bianchi type II solution, one generates a new solution with spikes
commonly observed in numerical simulations. It is conjectured that the spike
solution is part of the generalized Mixmaster attractor.Comment: Significantly revised. Colour figures simplified to accommodate
non-colour printin
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
Dynamical systems approach to G2 cosmology
In this paper we present a new approach for studying the dynamics of
spatially inhomogeneous cosmological models with one spatial degree of freedom.
By introducing suitable scale-invariant dependent variables we write the
evolution equations of the Einstein field equations as a system of autonomous
partial differential equations in first-order symmetric hyperbolic format,
whose explicit form depends on the choice of gauge. As a first application, we
show that the asymptotic behaviour near the cosmological initial singularity
can be given a simple geometrical description in terms of the local past
attractor on the boundary of the scale-invariant dynamical state space. The
analysis suggests the name ``asymptotic silence'' to describe the evolution of
the gravitational field near the cosmological initial singularity.Comment: 28 pages, 3 tables, 1 *.eps figure, LaTeX2e (10pt), matches version
accepted for publication by Classical and Quantum Gravit
Spherically symmetric relativistic stellar structures
We investigate relativistic spherically symmetric static perfect fluid models
in the framework of the theory of dynamical systems. The field equations are
recast into a regular dynamical system on a 3-dimensional compact state space,
thereby avoiding the non-regularity problems associated with the
Tolman-Oppenheimer-Volkoff equation. The global picture of the solution space
thus obtained is used to derive qualitative features and to prove theorems
about mass-radius properties. The perfect fluids we discuss are described by
barotropic equations of state that are asymptotically polytropic at low
pressures and, for certain applications, asymptotically linear at high
pressures. We employ dimensionless variables that are asymptotically homology
invariant in the low pressure regime, and thus we generalize standard work on
Newtonian polytropes to a relativistic setting and to a much larger class of
equations of state. Our dynamical systems framework is particularly suited for
numerical computations, as illustrated by several numerical examples, e.g., the
ideal neutron gas and examples that involve phase transitions.Comment: 23 pages, 25 figures (compressed), LaTe
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