2,938 research outputs found
The Gowdy T3 Cosmologies revisited
We have examined, repeated and extended earlier numerical calculations of
Berger and Moncrief for the evolution of unpolarized Gowdy T3 cosmological
models. Our results are consistent with theirs and we support their claim that
the models exhibit AVTD behaviour, even though spatial derivatives cannot be
neglected. The behaviour of the curvature invariants and the formation of
structure through evolution both backwards and forwards in time is discussed.Comment: 11 pages, LaTeX, 6 figures, results and conclusions revised and
(considerably) expande
A group selection perspective on economic behavior, institutions and organizations
This article examines the role of group dynamics and interactions in explaining economic behavior and the evolution of institutions. Our starting point is the large literature on group selection in the biological, behavioral and social sciences. We present a range of interpretations of group selection, describe a complete set of group selection mechanisms, and discuss the empirical and experimental evidence for group selection. Unique features of cultural group selection are investigated, and opportunities for applying the latter to various areas of economic theory and economic policy are identified
Locally U(1)*U(1) Symmetric Cosmological Models: Topology and Dynamics
We show examples which reveal influences of spatial topologies to dynamics,
using a class of spatially {\it closed} inhomogeneous cosmological models. The
models, called the {\it locally U(1)U(1) symmetric models} (or the {\it
generalized Gowdy models}), are characterized by the existence of two commuting
spatial {\it local} Killing vectors. For systematic investigations we first
present a classification of possible spatial topologies in this class. We
stress the significance of the locally homogeneous limits (i.e., the Bianchi
types or the `geometric structures') of the models. In particular, we show a
method of reduction to the natural reduced manifold, and analyze the
equivalences at the reduced level of the models as dynamical models. Based on
these fundamentals, we examine the influence of spatial topologies on dynamics
by obtaining translation and reflection operators which commute with the
dynamical flow in the phase space.Comment: 32 pages, 1 figure, LaTeX2e, revised Introduction slightly. To appear
in CQ
Coordinate Singularities in Harmonically-sliced Cosmologies
Harmonic slicing has in recent years become a standard way of prescribing the
lapse function in numerical simulations of general relativity. However, as was
first noticed by Alcubierre (1997), numerical solutions generated using this
slicing condition can show pathological behaviour. In this paper, analytic and
numerical methods are used to examine harmonic slicings of Kasner and Gowdy
cosmological spacetimes. It is shown that in general the slicings are prevented
from covering the whole of the spacetimes by the appearance of coordinate
singularities. As well as limiting the maximum running times of numerical
simulations, the coordinate singularities can lead to features being produced
in numerically evolved solutions which must be distinguished from genuine
physical effects.Comment: 21 pages, REVTeX, 5 figure
Numerical Investigation of Cosmological Singularities
Although cosmological solutions to Einstein's equations are known to be
generically singular, little is known about the nature of singularities in
typical spacetimes. It is shown here how the operator splitting used in a
particular symplectic numerical integration scheme fits naturally into the
Einstein equations for a large class of cosmological models and thus allows
study of their approach to the singularity. The numerical method also naturally
singles out the asymptotically velocity term dominated (AVTD) behavior known to
be characteristic of some of these models, conjectured to describe others, and
probably characteristic of a subclass of the rest. The method is first applied
to the unpolarized Gowdy T cosmology. Exact pseudo-unpolarized solutions
are used as a code test and demonstrate that a 4th order accurate
implementation of the numerical method yields acceptable agreement. For generic
initial data, support for the conjecture that the singularity is AVTD with
geodesic velocity (in the harmonic map target space) < 1 is found. A new
phenomenon of the development of small scale spatial structure is also
observed. Finally, it is shown that the numerical method straightforwardly
generalizes to an arbitrary cosmological spacetime on with one
spacelike U(1) symmetry.Comment: 37 pp +14 figures (not included, available on request), plain Te
5D gravitational waves from complexified black rings
In this paper we construct and briefly study the 5D time-dependent solutions
of general relativity obtained via double analytic continuation of the black
hole (Myers-Perry) and of the black ring solutions with a double
(Pomeransky-Senkov) and a single rotation (Emparan-Reall). The new solutions
take the form of a generalized Einstein-Rosen cosmology representing
gravitational waves propagating in a closed universe. In this context the
rotation parameters of the rings can be interpreted as the extra wave
polarizations, while it is interesting to state that the waves obtained from
Myers-Perry Black holes exhibit an extra boost-rotational symmetry in higher
dimensions which signals their better behavior at null infinity. The analogue
to the C-energy is analyzed.Comment: 18 pages, 4 figures. References added, introduction and conclusions
are amended, some issues related to singularity structure and symmetries are
discussed. Matches the print version to appear in JHE
Global existence problem in -Gowdy symmetric IIB superstring cosmology
We show global existence theorems for Gowdy symmetric spacetimes with type
IIB stringy matter. The areal and constant mean curvature time coordinates are
used. Before coming to that, it is shown that a wave map describes the
evolution of this system
High velocity spikes in Gowdy spacetimes
We study the behavior of spiky features in Gowdy spacetimes. Spikes with
velocity initially high are, generally, driven to low velocity. Let n be any
integer greater than or equal to 1. If the initial velocity of an upward
pointing spike is between 4n-3 and 4n-1 the spike persists with final velocity
between 1 and 2, while if the initial velocity is between 4n-1 and 4n+1, the
spiky feature eventually disappears. For downward pointing spikes the analogous
rule is that spikes with initial velocity between 4n-4 and 4n-2 persist with
final velocity between 0 and 1, while spikes with initial velocity between 4n-2
and 4n eventually disappear.Comment: discussion of constraints added. Accepted for publication in Phys.
Rev.
Time and "angular" dependent backgrounds from stationary axisymmetric solutions
Backgrounds depending on time and on "angular" variable, namely polarized and
unpolarized Gowdy models, are generated as the sector inside
the horizons of the manifold corresponding to axisymmetric solutions. As is
known, an analytical continuation of ordinary -branes, -branes allows
one to find -brane solutions. Simple models have been constructed by means
of analytic continuation of the Schwarzchild and the Kerr metrics. The
possibility of studying the -Gowdy models obtained here is outlined with an
eye toward seeing if they could represent some kind of generalized -branes
depending not only on time but also on an ``angular'' variable.Comment: 24 pages, 5 figures, corrected typos, references adde
Mixmaster Behavior in Inhomogeneous Cosmological Spacetimes
Numerical investigation of a class of inhomogeneous cosmological spacetimes
shows evidence that at a generic point in space the evolution toward the
initial singularity is asymptotically that of a spatially homogeneous spacetime
with Mixmaster behavior. This supports a long-standing conjecture due to
Belinskii et al. on the nature of the generic singularity in Einstein's
equations.Comment: 4 pages plus 4 figures. A sentence has been deleted. Accepted for
publication in PR
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