17 research outputs found
On the nature of initial singularities for solutions of the Einstein-Vlasov-scalar field system with surface symmetry
Global existence results in the past time direction of cosmological models
with collisionless matter and a massless scalar field are presented. It is
shown that the singularity is crushing and that the Kretschmann scalar diverges
uniformly as the singularity is approached. In the case without Vlasov matter,
the singularity is velocity dominated and the generalized Kasner exponents
converge at each spatial point as the singularity is approached
Local existence and continuation criteria for solutions of the Einstein-Vlasov-scalar field system with surface symmetry
We prove in the cases of spherical, plane and hyperbolic symmetry a local in
time existence theorem and continuation criteria for cosmological solutions of
the Einstein-Vlasov-scalar field system, with the sources generated by a
distribution function and a scalar field, subject to the Vlasov and wave
equations respectively. This system describes the evolution of self-gravitating
collisionless matter and scalar waves within the context of general relativity.
In the case where the only source is a scalar field it is shown that a global
existence result can be deduced from the general theorem.Comment: 33 pages, typos corrected, second conclusion of theorem 4.5 and
remark 4.6 remove
On the nature of initial singularities for solutions of the Einstein-Vlasov-scalar field system with surface symmetry
Global existence results in the past time direction of cosmological models with collisionless matter and a massless scalar field are presented. It is shown that the singularity is crushing and that the Kretschmann scalar diverges uniformly as the singularity is approached. In the case without Vlasov matter, the singularity is velocity dominated and the generalized Kasner exponents converge at each spatial point as the singularity is approached
Global existence and future asymptotic behaviour for solutions of the Einstein-Vlasov-scalar field system with surface symmetry
We prove in the cases of plane and hyperbolic symmetries a global in time
existence result in the future for comological solutions of the
Einstein-Vlasov-scalar field system, with the sources generated by a
distribution function and a scalar field, subject to the Vlasov and wave
equations respectively. The spacetime is future geodesically complete in the
special case of plane symmetry with only a scalar field. Causal geodesics are
also shown to be future complete for homogeneous solutions of the
Einstein-Vlasov-scalar field system with plane and hyperbolic symmetry.Comment: 14 page
Inextendibility of expanding cosmological models with symmetry
A new criterion for inextendibility of expanding cosmological models with
symmetry is presented. It is applied to derive a number of new results and to
simplify the proofs of existing ones. In particular it shows that the solutions
of the Einstein-Vlasov system with symmetry, including the vacuum
solutions, are inextendible in the future. The technique introduced adds a
qualitatively new element to the available tool-kit for studying strong cosmic
censorship.Comment: 7 page
Strong cosmic censorship for solutions of the Einstein-Maxwell field equations with polarized Gowdy symmetry
A proof of strong cosmic censorship is presented for a class of solutions of
the Einstein-Maxwell equations, those with polarized Gowdy symmetry. A key
element of the argument is the observation that by means of a suitable choice
of variables the central equations in this problem can be written in a form
where they are identical to the central equations for general (i.e.
non-polarized) vacuum Gowdy spacetimes. Using this it is seen that the deep
results of Ringstr\"om on strong cosmic censorship in the vacuum case have
implications for the Einstein-Maxwell case. Working out the geometrical meaning
of these analytical results leads to the main conclusion.Comment: Some references have been change
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-