755 research outputs found
Future non-linear stability for reflection symmetric solutions of the Einstein-Vlasov system of Bianchi types II and VI
Using the methods developed for the Bianchi I case we have shown that a
boostrap argument is also suitable to treat the future non-linear stability for
reflection symmetric solutions of the Einstein-Vlasov system of Bianchi types
II and VI. These solutions are asymptotic to the Collins-Stewart solution
with dust and the Ellis-MacCallum solution respectively. We have thus
generalized the results obtained by Rendall and Uggla in the case of locally
rotationally symmetric Bianchi II spacetimes to the reflection symmetric case.
However we needed to assume small data. For Bianchi VI there is no
analogous previous result.Comment: 30 page
A global foliation of Einstein-Euler spacetimes with Gowdy-symmetry on T3
We investigate the initial value problem for the Einstein-Euler equations of
general relativity under the assumption of Gowdy symmetry on T3, and we
construct matter spacetimes with low regularity. These spacetimes admit, both,
impulsive gravitational waves in the metric (for instance, Dirac mass curvature
singularities propagating at light speed) and shock waves in the fluid (i.e.,
discontinuities propagating at about the sound speed). Given an initial data
set, we establish the existence of a future development and we provide a global
foliation in terms of a globally and geometrically defined time-function,
closely related to the area of the orbits of the symmetry group. The main
difficulty lies in the low regularity assumed on the initial data set which
requires a distributional formulation of the Einstein-Euler equations.Comment: 24 page
Fuchsian methods and spacetime singularities
Fuchsian methods and their applications to the study of the structure of
spacetime singularities are surveyed. The existence question for spacetimes
with compact Cauchy horizons is discussed. After some basic facts concerning
Fuchsian equations have been recalled, various ways in which these equations
have been applied in general relativity are described. Possible future
applications are indicated
Late-time oscillatory behaviour for self-gravitating scalar fields
This paper investigates the late-time behaviour of certain cosmological
models where oscillations play an essential role. Rigorous results are proved
on the asymptotics of homogeneous and isotropic spacetimes with a linear
massive scalar field as source. Various generalizations are obtained for
nonlinear massive scalar fields, -essence models and gravity. The
effect of adding ordinary matter is discussed as is the case of nonlinear
scalar fields whose potential has a degenerate zero.Comment: 17 pages, additional reference
Dynamics of spatially homogeneous solutions of the Einstein-Vlasov equations which are locally rotationally symmetric
The dynamics of a class of cosmological models with collisionless matter and
four Killing vectors is studied in detail and compared with that of
corresponding perfect fluid models. In many cases it is possible to identify
asymptotic states of the spacetimes near the singularity or in a phase of
unlimited expansion. Bianchi type II models show oscillatory behaviour near the
initial singularity which is, however, simpler than that of the mixmaster
model.Comment: 27 pages, 3 figures, LaTe
Intermediate inflation and the slow-roll approximation
It is shown that spatially homogeneous solutions of the Einstein equations
coupled to a nonlinear scalar field and other matter exhibit accelerated
expansion at late times for a wide variety of potentials . These potentials
are strictly positive but tend to zero at infinity. They satisfy restrictions
on and related to the slow-roll approximation. These results
generalize Wald's theorem for spacetimes with positive cosmological constant to
those with accelerated expansion driven by potentials belonging to a large
class.Comment: 19 pages, results unchanged, additional backgroun
The Einstein-Vlasov sytem/Kinetic theory
The main purpose of this article is to guide the reader 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 where the main focus has
been on nonrelativistic- and special relativistic physics, e.g. 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. The Vlasov equation describes matter
phenomenologically and it should be stressed that most of the theorems
presented in this article are not presently known for other such matter models
(e.g. fluid models). The first part of this paper gives an introduction to
kinetic theory in non-curved spacetimes and then the Einstein-Vlasov system is
introduced. We believe that a good understanding of kinetic theory in
non-curved spacetimes is fundamental in order to get a good comprehension of
kinetic theory in general relativity.Comment: 31 pages. This article has been submitted to Living Rev. Relativity
(http://www.livingreviews.org
Algebraic expansions for curvature coupled scalar field models
A late time asymptotic perturbative analysis of curvature coupled complex
scalar field models with accelerated cosmological expansion is carried out on
the level of formal power series expansions. For this, algebraic analogues of
the Einstein scalar field equations in Gaussian coordinates for space-time
dimensions greater than two are postulated and formal solutions are constructed
inductively and shown to be unique. The results obtained this way are found to
be consistent with already known facts on the asymptotics of such models. In
addition, the algebraic expansions are used to provide a prospect of the large
time behaviour that might be expected of the considered models.Comment: 16 pages, no figures; v2: typos corrected, 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
Cosmological spacetimes not covered by a constant mean curvature slicing
We show that there exist maximal globally hyperbolic solutions of the
Einstein-dust equations which admit a constant mean curvature Cauchy surface,
but are not covered by a constant mean curvature foliation.Comment: 11 page
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