2,306 research outputs found
Global existence for the spherically symmetric Einstein-Vlasov system with outgoing matter
We prove a new global existence result for the asymptotically flat,
spherically symmetric Einstein-Vlasov system which describes in the framework
of general relativity an ensemble of particles which interact by gravity. The
data are such that initially all the particles are moving radially outward and
that this property can be bootstrapped. The resulting non-vacuum spacetime is
future geodesically complete.Comment: 16 page
Existence of axially symmetric static solutions of the Einstein-Vlasov system
We prove the existence of static, asymptotically flat non-vacuum spacetimes
with axial symmetry where the matter is modeled as a collisionless gas. The
axially symmetric solutions of the resulting Einstein-Vlasov system are
obtained via the implicit function theorem by perturbing off a suitable
spherically symmetric steady state of the Vlasov-Poisson system.Comment: 32 page
Spherically symmetric steady states of galactic dynamics in scalar gravity
The kinetic motion of the stars of a galaxy is considered within the
framework of a relativistic scalar theory of gravitation. This model, even
though unphysical, may represent a good laboratory where to study in a
rigorous, mathematical way those problems, like the influence of the
gravitational radiation on the dynamics, which are still beyond our present
understanding of the physical model represented by the Einstein--Vlasov system.
The present paper is devoted to derive the equations of the model and to prove
the existence of spherically symmetric equilibria with finite radius.Comment: 13 pages, mistypos correcte
Global existence of classical solutions to the Vlasov-Poisson system in a three dimensional, cosmological setting
The initial value problem for the Vlasov-Poisson system is by now well
understood in the case of an isolated system where, by definition, the
distribution function of the particles as well as the gravitational potential
vanish at spatial infinity. Here we start with homogeneous solutions, which
have a spatially constant, non-zero mass density and which describe the mass
distribution in a Newtonian model of the universe. These homogeneous states can
be constructed explicitly, and we consider deviations from such homogeneous
states, which then satisfy a modified version of the Vlasov-Poisson system. We
prove global existence and uniqueness of classical solutions to the
corresponding initial value problem for initial data which represent spatially
periodic deviations from homogeneous states.Comment: 23 pages, Latex, report #
A non-variational approach to nonlinear stability in stellar dynamics applied to the King model
In previous work by Y. Guo and G. Rein, nonlinear stability of equilibria in
stellar dynamics, i.e., of steady states of the Vlasov-Poisson system, was
accessed by variational techniques. Here we propose a different,
non-variational technique and use it to prove nonlinear stability of the King
model against a class of spherically symmetric, dynamically accessible
perturbations. This model is very important in astrophysics and was out of
reach of the previous techniques
A numerical investigation of the stability of steady states and critical phenomena for the spherically symmetric Einstein-Vlasov system
The stability features of steady states of the spherically symmetric
Einstein-Vlasov system are investigated numerically. We find support for the
conjecture by Zeldovich and Novikov that the binding energy maximum along a
steady state sequence signals the onset of instability, a conjecture which we
extend to and confirm for non-isotropic states. The sign of the binding energy
of a solution turns out to be relevant for its time evolution in general. We
relate the stability properties to the question of universality in critical
collapse and find that for Vlasov matter universality does not seem to hold.Comment: 29 pages, 10 figure
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
Regularity results for the spherically symmetric Einstein-Vlasov system
The spherically symmetric Einstein-Vlasov system is considered in
Schwarzschild coordinates and in maximal-isotropic coordinates. An open problem
is the issue of global existence for initial data without size restrictions.
The main purpose of the present work is to propose a method of approach for
general initial data, which improves the regularity of the terms that need to
be estimated compared to previous methods. We prove that global existence holds
outside the centre in both these coordinate systems. In the Schwarzschild case
we improve the bound on the momentum support obtained in \cite{RRS} for compact
initial data. The improvement implies that we can admit non-compact data with
both ingoing and outgoing matter. This extends one of the results in
\cite{AR1}. In particular our method avoids the difficult task of treating the
pointwise matter terms. Furthermore, we show that singularities never form in
Schwarzschild time for ingoing matter as long as This removes an
additional assumption made in \cite{A1}. Our result in maximal-isotropic
coordinates is analogous to the result in \cite{R1}, but our method is
different and it improves the regularity of the terms that need to be estimated
for proving global existence in general.Comment: 25 pages. To appear in Ann. Henri Poincar\'
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