43 research outputs found
On the area of the symmetry orbits in symmetric spacetimes
We obtain a global existence result for the Einstein equations. We show that
in the maximal Cauchy development of vacuum symmetric initial data with
nonvanishing twist constant, except for the special case of flat Kasner initial
data, the area of the group orbits takes on all positive values. This
result shows that the areal time coordinate which covers these spacetimes
runs from zero to infinity, with the singularity occurring at R=0.Comment: The appendix which appears in version 1 has a technical problem (the
inequality appearing as the first stage of (52) is not necessarily true), and
since the appendix is unnecessary for the proof of our results, we leave it
out. version 2 -- clarifications added, version 3 -- reference correcte
On the area of the symmetry orbits in symmetric spacetimes with Vlasov matter
This paper treats the global existence question for a collection of general
relativistic collisionless particles, all having the same mass. The spacetimes
considered are globally hyperbolic, with Cauchy surface a 3-torus. Furthermore,
the spacetimes considered are isometrically invariant under a two-dimensional
group action, the orbits of which are spacelike 2-tori. It is known from
previous work that the area of the group orbits serves as a global time
coordinate. In the present work it is shown that the area takes on all positive
values in the maximal Cauchy development.Comment: 27 pages, version 2 minor changes and correction
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.
Nonlinear spinor field in cosmology
Within the scope of Bianchi type VI (BVI) model the self-consistent system of
nonlinear spinor and gravitational fields is considered. Exact self-consistent
solutions to the spinor and gravitational field equations are obtained for some
special choice of spatial inhomogeneity and nonlinear spinor term. The role of
inhomogeneity in the evolution of spinor and gravitational field is studied.
Oscillatory mode of expansion of the BVI universe is obtained for some special
choice of spinor field nonlinearity.Comment: RevTex4, 19 pages, 4 figure
Manufacture of Gowdy spacetimes with spikes
In numerical studies of Gowdy spacetimes evidence has been found for the
development of localized features (spikes) involving large gradients near the
singularity. The rigorous mathematical results available up to now did not
cover this kind of situation. In this work we show the existence of large
classes of Gowdy spacetimes exhibiting features of the kind discovered
numerically. These spacetimes are constructed by applying certain
transformations to previously known spacetimes without spikes. It is possible
to control the behaviour of the Kretschmann scalar near the singularity in
detail. This curvature invariant is found to blow up in a way which is
non-uniform near the spike in some cases. When this happens it demonstrates
that the spike is a geometrically invariant feature and not an artefact of the
choice of variables used to parametrize the metric. We also identify another
class of spikes which are artefacts. The spikes produced by our method are
compared with the results of numerical and heuristic analyses of the same
situation.Comment: 25 page
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
Epigenetic and Genetic Factors Predict Women's Salivary Cortisol following a Threat to the Social Self
10.1371/journal.pone.0048597PLoS ONE711
DEAR1 Is a Dominant Regulator of Acinar Morphogenesis and an Independent Predictor of Local Recurrence-Free Survival in Early-Onset Breast Cancer
Ann Killary and colleagues describe a new gene that is genetically altered in breast tumors, and that may provide a new breast cancer prognostic marker