1,455 research outputs found
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
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
On static shells and the Buchdahl inequality for the spherically symmetric Einstein-Vlasov system
In a previous work \cite{An1} matter models such that the energy density
and the radial- and tangential pressures and
satisfy were considered in the context of
Buchdahl's inequality. It was proved that static shell solutions of the
spherically symmetric Einstein equations obey a Buchdahl type inequality
whenever the support of the shell, satisfies
Moreover, given a sequence of solutions such that then the
limit supremum of was shown to be bounded by
In this paper we show that the hypothesis
that can be realized for Vlasov matter, by constructing a
sequence of static shells of the spherically symmetric Einstein-Vlasov system
with this property. We also prove that for this sequence not only the limit
supremum of is bounded, but that the limit is
since for Vlasov matter.
Thus, static shells of Vlasov matter can have arbitrary close to
which is interesting in view of \cite{AR2}, where numerical evidence is
presented that 8/9 is an upper bound of of any static solution of the
spherically symmetric Einstein-Vlasov system.Comment: 20 pages, Late
Resonance production by neutrinos: I. J=3/2 Resonances
The article contains general formulas for the production of J=3/2 resonances
by neutrinos and antineutrinos. It specializes to the P_{33}(1232) resonance
whose form factors are determined by theory and experiment and then are
compared with experimental results at low and high energies. It is shown that
the minimum in the low Q^2 region is a consequence of a combined effect from
the vanishing of the vector form factors, the muon mass and Pauli blocking.
Several improvements for the future investigations are suggested.Comment: 10 pages, LaTeX, misprints corrected, 1 reference adde
Stable Models of Elliptical Galaxies
We construct stable axially symmetric models of elliptical galaxies. The
particle density on phase space for these models depends monotonically on the
particle energy and on the third component of the angular momentum. They are
obtained as minimizers of suitably defined energy-Casimir functionals, and this
implies their nonlinear stability. Since our analysis proceeds from a rigorous
but purely mathematical point of view it should be interesting to determine if
any of our models match observational data in astrophysics. The main purpose of
these notes is to initiate some exchange of information between the
astrophysics and the mathematics communities.Comment: 26 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)
On two weak CC Delta production models
We perform a detail analysis of two models of neutrino CC Delta production on
free nucleons. First model is a standard one based on nucleon-Delta transition
current with several form-factors. Second model is a starting point for a
construction of Marteau model with sophisticated analytical computations of
nuclear effects. We conclude that both models lead to similar results.Comment: 9 pages, includes 9 figures, accepted for publication in J. Phys.
Higher Twist, Scaling, and Effective for Lepton Scattering in the Few GeV Region
We use a new scaling variable , and add low modifications to
GRV98 leading order parton distribution functions such that they can be used to
model electron, muon and neutrino inelastic scattering cross sections (and also
photoproduction) at both very low and high energies.Comment: 6 pages, 3 figures. To be published in J. Phys. G (Conf. Proceedings)
based on two talks by Arie Bodek at the NuFact conference, Imperial
College, London, England, July 200
Black holes vs. naked singularities formation in collapsing Einstein's clusters
Non-static, spherically symmetric clusters of counter-rotating particles, of
the type first introduced by Einstein, are analysed here. The initial data
space can be parameterized in terms of three arbitrary functions, namely;
initial density, velocity and angular momentum profiles. The final state of
collapse, black hole or naked singularity, turns out to depend on the order of
the first non-vanishing derivatives of such functions at the centre. The work
extends recent results by Harada, Iguchi and Nakao.Comment: 13 pages, LaTeX format. To appear in Physical Review
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