2,461 research outputs found
Spherically symmetric equilibria for self-gravitating kinetic or fluid models in the non-relativistic and relativistic case - A simple proof for finite extension
We consider a self-gravitating collisionless gas as described by the
Vlasov-Poisson or Einstein-Vlasov system or a self-gravitating fluid ball as
described by the Euler-Poisson or Einstein-Euler system. We give a simple proof
for the finite extension of spherically symmetric equilibria, which covers all
these models simultaneously. In the Vlasov case the equilibria are
characterized by a local growth condition on the microscopic equation of state,
i.e., on the dependence of the particle distribution on the particle energy, at
the cut-off energy E_0, and in the Euler case by the corresponding growth
condition on the equation of state p=P(\rho) at \rho=0. These purely local
conditions are slight generalizations to known such conditions.Comment: 20 page
On the steady states of the spherically symmetric Einstein-Vlasov system
Using both numerical and analytical tools we study various features of
static, spherically symmetric solutions of the Einstein-Vlasov system. In
particular, we investigate the possible shapes of their mass-energy density and
find that they can be multi-peaked, we give numerical evidence and a partial
proof for the conjecture that the Buchdahl inequality , the quasi-local mass, holds for all such steady states--both
isotropic {\em and} anisotropic--, and we give numerical evidence and a partial
proof for the conjecture that for any given microscopic equation of state--both
isotropic {\em and} anisotropic--the resulting one-parameter family of static
solutions generates a spiral in the radius-mass diagram.Comment: 34 pages, 18 figures, LaTe
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 #
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
Appearance of quark-hadron duality in the Rein-Sehgal model
Quark-hadron duality in neutrino-nucleon reactions is investigated under the
assumption that cross sections in the resonance region are given by the
Rein-Sehgal model. The quantitative analysis of the duality is done by means of
appropriate integrals of the structure functions in the Nachtmann variable. We
conclude that with the definition of the resonance region
GeV) the duality holds for neutrino-proton reaction structure function
for GeV and it is absent for neutrino-neutron reaction.Comment: 4 pages, 7 figures, presented at NuInt05 conference, Okayama, Sept.
26-29, 200
Static cylindrically symmetric spacetimes
We prove existence of static solutions to the cylindrically symmetric
Einstein-Vlasov system, and we show that the matter cylinder has finite
extension. The same results are also proved for a quite general class of
equations of state for perfect fluids coupled to the Einstein equations,
extending the class of equations of state considered in \cite{BL}. We also
obtain this result for the Vlasov-Poisson system.Comment: Added acknowledgemen
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
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