9 research outputs found
The plane symmetric Einstein-dust system with positive cosmological constant
The Einstein equations with a positive cosmological constant are coupled to
the pressureless perfect fluid matter in plane symmetry. Under suitable
restrictions on the initial data, the resulting Einstein-dust system is proved
to have a global classical solution in the future time direction. Some late
time asymptotic properties are obtained as well.Comment: 12 page
Areal Foliation and AVTD Behavior in T^2 Symmetric Spacetimes with Positive Cosmological Constant
We prove a global foliation result, using areal time, for T^2 symmetric
spacetimes with a positive cosmological constant. We then find a class of
solutions that exhibit AVTD behavior near the singularity.Comment: 15 pages, 0 figures, 2 references adde
Global existence and asymptotic behaviour in the future for the Einstein-Vlasov system with positive cosmological constant
The behaviour of expanding cosmological models with collisionless matter and
a positive cosmological constant is analysed. It is shown that under the
assumption of plane or hyperbolic symmetry the area radius goes to infinity,
the spacetimes are future geodesically complete, and the expansion becomes
isotropic and exponential at late times. This proves a form of the cosmic no
hair theorem in this class of spacetimes
Accelerated cosmological expansion due to a scalar field whose potential has a positive lower bound
In many cases a nonlinear scalar field with potential can lead to
accelerated expansion in cosmological models. This paper contains mathematical
results on this subject for homogeneous spacetimes. It is shown that, under the
assumption that has a strictly positive minimum, Wald's theorem on
spacetimes with positive cosmological constant can be generalized to a wide
class of potentials. In some cases detailed information on late-time
asymptotics is obtained. Results on the behaviour in the past time direction
are also presented.Comment: 16 page
Theorems on existence and global dynamics for the Einstein equations
This article is a guide to theorems on existence and global dynamics of
solutions of the Einstein equations. It draws attention to open questions in
the field. The local-in-time Cauchy problem, which is relatively well
understood, is surveyed. Global results for solutions with various types of
symmetry are discussed. A selection of results from Newtonian theory and
special relativity that offer useful comparisons is presented. Treatments of
global results in the case of small data and results on constructing spacetimes
with prescribed singularity structure or late-time asymptotics are given. A
conjectural picture of the asymptotic behaviour of general cosmological
solutions of the Einstein equations is built up. Some miscellaneous topics
connected with the main theme are collected in a separate section.Comment: Submitted to Living Reviews in Relativity, major update of Living
Rev. Rel. 5 (2002)
The Einstein-Vlasov System/Kinetic Theory
The main purpose of this article is to provide a guide to theorems on global
properties of solutions to the Einstein--Vlasov system. This system couples
Einstein's equations to a kinetic matter model. Kinetic theory has been an
important field of research during several decades in which the main focus has
been on non-relativistic and special relativistic physics, i.e., to model the
dynamics of neutral gases, plasmas, and Newtonian self-gravitating systems. In
1990, Rendall and Rein initiated a mathematical study of the Einstein--Vlasov
system. Since then many theorems on global properties of solutions to this
system have been established.Comment: Published version http://www.livingreviews.org/lrr-2011-