947 research outputs found
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
Late-time behaviour of the Einstein-Vlasov system with Bianchi I symmetry
The late-time behaviour of the Einstein-dust system is well understood for
homogeneous spacetimes. For the case of Bianchi I we have been able to show
that the late-time behaviour of the Einstein-Vlasov system is well approximated
by the Einstein-dust system assuming that one is close to the unique stationary
solution which is the attractor of the Einstein-dust system.Comment: 4 pages, based on a talk given at the Spanish Relativity Meeting
2010, to appear in Journal of Physics: Conference Series (JPCS
Late-time behaviour of the Einstein-Vlasov system with Bianchi I symmetry
The late-time behaviour of the Einstein-dust system is well understood for
homogeneous spacetimes. For the case of Bianchi I we have been able to show
that the late-time behaviour of the Einstein-Vlasov system is well approximated
by the Einstein-dust system assuming that one is close to the unique stationary
solution which is the attractor of the Einstein-dust system.Comment: 4 pages, based on a talk given at the Spanish Relativity Meeting
2010, to appear in Journal of Physics: Conference Series (JPCS
A class of dust-like self-similar solutions of the massless Einstein-Vlasov system
In this paper the existence of a class of self-similar solutions of the
Einstein-Vlasov system is proved. The initial data for these solutions are not
smooth, with their particle density being supported in a submanifold of
codimension one. They can be thought of as intermediate between smooth
solutions of the Einstein-Vlasov system and dust. The motivation for studying
them is to obtain insights into possible violation of weak cosmic censorship by
solutions of the Einstein-Vlasov system. By assuming a suitable form of the
unknowns it is shown that the existence question can be reduced to that of the
existence of a certain type of solution of a four-dimensional system of
ordinary differential equations depending on two parameters. This solution
starts at a particular point and converges to a stationary solution
as the independent variable tends to infinity. The existence proof is based on
a shooting argument and involves relating the dynamics of solutions of the
four-dimensional system to that of solutions of certain two- and
three-dimensional systems obtained from it by limiting processes.Comment: 47 page
Fuchsian methods and spacetime singularities
Fuchsian methods and their applications to the study of the structure of
spacetime singularities are surveyed. The existence question for spacetimes
with compact Cauchy horizons is discussed. After some basic facts concerning
Fuchsian equations have been recalled, various ways in which these equations
have been applied in general relativity are described. Possible future
applications are indicated
On the area of the symmetry orbits in symmetric spacetimes with Vlasov matter
This paper treats the global existence question for a collection of general
relativistic collisionless particles, all having the same mass. The spacetimes
considered are globally hyperbolic, with Cauchy surface a 3-torus. Furthermore,
the spacetimes considered are isometrically invariant under a two-dimensional
group action, the orbits of which are spacelike 2-tori. It is known from
previous work that the area of the group orbits serves as a global time
coordinate. In the present work it is shown that the area takes on all positive
values in the maximal Cauchy development.Comment: 27 pages, version 2 minor changes and correction
Late-time oscillatory behaviour for self-gravitating scalar fields
This paper investigates the late-time behaviour of certain cosmological
models where oscillations play an essential role. Rigorous results are proved
on the asymptotics of homogeneous and isotropic spacetimes with a linear
massive scalar field as source. Various generalizations are obtained for
nonlinear massive scalar fields, -essence models and gravity. The
effect of adding ordinary matter is discussed as is the case of nonlinear
scalar fields whose potential has a degenerate zero.Comment: 17 pages, additional reference
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