13,679 research outputs found
Cosmological solutions of the Vlasov-Einstein system with spherical, plane, and hyperbolic symmetry
The Vlasov-Einstein system describes a self-gravitating, collisionless gas
within the framework of general relativity. We investigate the initial value
problem in a cosmological setting with spherical, plane, or hyperbolic symmetry
and prove that for small initial data solutions exist up to a spacetime
singularity which is a curvature and a crushing singularity. An important tool
in the analysis is a local existence result with a continuation criterion
saying that solutions can be extended as long as the momenta in the support of
the phase-space distribution of the matter remain bounded.Comment: 32 pages, LaTeX, report 94
PCAC and the Deficit of Forward Muons in pi^+ Production by Neutrinos
The K2K experiment, using a fine-grained detector in a neutrino beam of
energy has observed two-track events that can be
interpreted as a coherent reaction or an incoherent process , the final nucleon being unobserved. The data show a significant
deficit of forward-going muons in the interval ,
where a sizeable coherent signal is expected. We attempt an explanantion of
this effect, using a PCAC formula that includes the effect of the non-vanishing
muon mass. A suppression of about 25 % is caused by a destructive interference
of the axial vector and pseudoscalar (pion-exchange) amplitudes. The incoherent
background is also reduced by 10 - 15 %. As a consequence the discrepancy
between theory and observation is significantly reduced.Comment: 4 pages including 1 figure, changes in abstract and text; version to
appear in Phys.Lett.
On future geodesic completeness for the Einstein-Vlasov system with hyperbolic symmetry
Spacetimes with collisionless matter evolving from data on a compact Cauchy
surface with hyperbolic symmetry are shown to be timelike and null geodesically
complete in the expanding direction, provided the data satisfy a certain size
restriction.Comment: 8 page
Flat steady states in stellar dynamics - existence and stability
We consider a special case of the three dimensional Vlasov-Poisson system
where the particles are restricted to a plane, a situation that is used in
astrophysics to model extremely flattened galaxies. We prove the existence of
steady states of this system. They are obtained as minimizers of an
energy-Casimir functional from which fact a certain dynamical stability
property is deduced. From a mathematics point of view these steady states
provide examples of partially singular solutions of the three dimensional
Vlasov-Poisson system.Comment: 25 pages, LaTe
Non-linear stability of gaseous stars
We construct steady states of the Euler-Poisson system with a barotropic
equation of state as minimizers of a suitably defined energy functional. Their
minimizing property implies the non-linear stability of such states against
general, i.e., not necessarily spherically symmetric perturbations. The
mathematical approach is based on previous stability results for the
Vlasov-Poisson system by Y. Guo and the author, exploiting the energy-Casimir
technique. The analysis is conditional in the sense that it assumes the
existence of solutions to the initial value problem for the Euler-Poisson
system which preserve mass and energy. The relation between the Euler-Poisson
and the Vlasov-Poisson system in this context is also explored.Comment: 18 pages, LaTe
Nonlinear stability of homogeneous models in Newtonian cosmology
We consider the Vlasov-Poisson system in a cosmological setting and prove
nonlinear stability of homogeneous solutions against small, spatially periodic
perturbations in the sup-norm of the spatial mass density. This result is
connected with the question of how large scale structures such as galaxies have
evolved out of the homogeneous state of the early universe.Comment: 19 pages, late
Static shells for the Vlasov-Poisson and Vlasov-Einstein systems
We prove the existence of static, spherically symmetric solutions of the
stellar dynamic Vlasov-Poisson and Vlasov-Einstein systems, which have the
property that their spatial support is a finite, spherically symmetric shell
with a vacuum region at the center.Comment: 14 pages, LaTe
Stability of spherically symmetric steady states in galactic dynamics against general perturbations
Certain steady states of the Vlasov-Poisson system can be characterized as
minimizers of an energy-Casimir functional, and this fact implies a nonlinear
stability property of such steady states. In previous investigations by Y. Guo
and the author stability was obtained only with respect to spherically
symmetric perturbations. In the present investigation we show how to remove
this unphysical restriction.Comment: 19 pages LaTe
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