3,866 research outputs found
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
Formation of trapped surfaces for the spherically symmetric Einstein-Vlasov system
We consider the spherically symmetric, asymptotically flat, non-vacuum
Einstein equations, using as matter model a collisionless gas as described by
the Vlasov equation. We find explicit conditions on the initial data which
guarantee the formation of a trapped surface in the evolution which in
particular implies that weak cosmic censorship holds for these data. We also
analyze the evolution of solutions after a trapped surface has formed and we
show that the event horizon is future complete. Furthermore we find that the
apparent horizon and the event horizon do not coincide. This behavior is
analogous to what is found in certain Vaidya spacetimes. The analysis is
carried out in Eddington-Finkelstein coordinates.Comment: 2
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 #
Stochastic orbital migration of small bodies in Saturn's rings
Many small moonlets, creating propeller structures, have been found in
Saturn's rings by the Cassini spacecraft. We study the dynamical evolution of
such 20-50m sized bodies which are embedded in Saturn's rings. We estimate the
importance of various interaction processes with the ring particles on the
moonlet's eccentricity and semi-major axis analytically. For low ring surface
densities, the main effects on the evolution of the eccentricity and the
semi-major axis are found to be due to collisions and the gravitational
interaction with particles in the vicinity of the moonlet. For large surface
densities, the gravitational interaction with self-gravitating wakes becomes
important.
We also perform realistic three dimensional, collisional N-body simulations
with up to a quarter of a million particles. A new set of pseudo shear periodic
boundary conditions is used which reduces the computational costs by an order
of magnitude compared to previous studies. Our analytic estimates are confirmed
to within a factor of two.
On short timescales the evolution is always dominated by stochastic effects
caused by collisions and gravitational interaction with self-gravitating ring
particles. These result in a random walk of the moonlet's semi-major axis. The
eccentricity of the moonlet quickly reaches an equilibrium value due to
collisional damping. The average change in semi-major axis of the moonlet after
100 orbital periods is 10-100m. This translates to an offset in the azimuthal
direction of several hundred kilometres. We expect that such a shift is easily
observable.Comment: 13 pages, 6 figures, submitted to A&A, comments welcom
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
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
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
Flat galaxies with dark matter halos - existence and stability
We consider a model for a flat, disk-like galaxy surrounded by a halo of dark
matter, namely a Vlasov-Poisson type system with two particle species, the
stars which are restricted to the galactic plane and the dark matter particles.
These constituents interact only through the gravitational potential which
stars and dark matter create collectively. Using a variational approach we
prove the existence of steady state solutions and their nonlinear stability
under suitably restricted perturbations.Comment: 39 page
Dynamical Stability of Imaged Planetary Systems in Formation: Application to HL Tau
A recent ALMA image revealed several concentric gaps in the protoplanetary
disk surrounding the young star HL Tau. We consider the hypothesis that these
gaps are carved by planets, and present a general framework for understanding
the dynamical stability of such systems over typical disk lifetimes, providing
estimates for the maximum planetary masses. We collect these easily evaluated
constraints into a workflow that can help guide the design and interpretation
of new observational campaigns and numerical simulations of gap opening in such
systems. We argue that the locations of resonances should be significantly
shifted in massive disks like HL Tau, and that theoretical uncertainties in the
exact offset, together with observational errors, imply a large uncertainty in
the dynamical state and stability in such disks. This presents an important
barrier to using systems like HL Tau as a proxy for the initial conditions
following planet formation. An important observational avenue to breaking this
degeneracy is to search for eccentric gaps, which could implicate resonantly
interacting planets. Unfortunately, massive disks like HL Tau should induce
swift pericenter precession that would smear out any such eccentric features of
planetary origin. This motivates pushing toward more typical, less massive
disks. For a nominal non-resonant model of the HL Tau system with five planets,
we find a maximum mass for the outer three bodies of approximately 2 Neptune
masses. In a resonant configuration, these planets can reach at least the mass
of Saturn. The inner two planets' masses are unconstrained by dynamical
stability arguments.Comment: Accepted in ApJ. 16 pages 8 figure
Tau Appearance In Atmospheric Neutrino Interactions
If the correct interpretation of the Super-Kamiokande atmospheric neutrino
data is \nu_\mu -> \nu_\tau oscillation, the contained data sample should
already have more than 10 tau appearance events. We study the challenging task
of detecting the tau, focussing on the decay chain \tau^\pm -> \rho^\pm ->
\pi^\pm \pi^0 in events with quasi-elastic tau production. The background
level, which is currently quite uncertain because of a lack of relevant neutral
current data, can be measured by the near detector in the K2K experiment. Our
estimates of the background suggest that it may be possible to detect tau
appearance in Super-Kamiokande with 5-10 years of running.Comment: 13 pages, uses psfi
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