940 research outputs found
Constant mean curvature slicings of Kantowski-Sachs spacetimes
We investigate existence, uniqueness, and the asymptotic properties of
constant mean curvature (CMC) slicings in vacuum Kantowski-Sachs spacetimes
with positive cosmological constant. Since these spacetimes violate the strong
energy condition, most of the general theorems on CMC slicings do not apply.
Although there are in fact Kantowski-Sachs spacetimes with a unique CMC
foliation or CMC time function, we prove that there also exist Kantowski-Sachs
spacetimes with an arbitrary number of (families of) CMC slicings. The
properties of these slicings are analyzed in some detail
Bouncing Palatini cosmologies and their perturbations
Nonsingular cosmologies are investigated in the framework of f(R) gravity
within the first order formalism. General conditions for bounces in isotropic
and homogeneous cosmology are presented. It is shown that only a quadratic
curvature correction is needed to predict a bounce in a flat or to describe
cyclic evolution in a curved dust-filled universe. Formalism for perturbations
in these models is set up. In the simplest cases, the perturbations diverge at
the turnover. Conditions to obtain smooth evolution are derived.Comment: 7 pages, 1 figure. v2: added references
Bianchi Cosmologies with Anisotropic Matter: Locally Rotationally Symmetric Models
The dynamics of cosmological models with isotropic matter sources (perfect
fluids) is extensively studied in the literature; in comparison, the dynamics
of cosmological models with anisotropic matter sources is not. In this paper we
consider spatially homogeneous locally rotationally symmetric solutions of the
Einstein equations with a large class of anisotropic matter models including
collisionless matter (Vlasov), elastic matter, and magnetic fields. The
dynamics of models of Bianchi types I, II, and IX are completely described; the
two most striking results are the following: (i) There exist matter models,
compatible with the standard energy conditions, such that solutions of Bianchi
type IX (closed cosmologies) need not necessarily recollapse; there is an open
set of forever expanding solutions. (ii) Generic type IX solutions associated
with a matter model like Vlasov matter exhibit oscillatory behavior toward the
initial singularity. This behavior differs significantly from that of
vacuum/perfect fluid cosmologies; hence "matter matters". Finally, we indicate
that our methods can probably be extended to treat a number of open problems,
in particular, the dynamics of Bianchi type VIII and Kantowski-Sachs solutions.Comment: 64 pages, 19 Figure
Self-gravitating Newtonian disks revisited
Recent analytic results concerning stationary, self-gravitating fluids in
Newtonian theory are discussed. We give a theorem that forbids infinitely
extended fluids, depending on the assumed equation of state and the rotation
law. This part extends previous results that have been obtained for static
configurations. The second part discusses a Sobolev bound on the mass of the
fluid and a rigorous Jeans-type inequality that is valid in the stationary
case.Comment: A talk given at the Spanish Relativity Meeting in Portugal 2012. To
appear in Progress in Mathematical Relativity, Gravitation and Cosmology,
Proceedings of the Spanish Relativity Meeting ERE2012, University of Minho,
Guimaraes, Portugal, 3-7 September 2012, Springer Proceedings in Mathematics
& Statistics, Vol. 6
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