507 research outputs found
On the Einstein-Vlasov system with hyperbolic symmetry
It is shown that a spacetime with collisionless matter evolving from data on a compact Cauchy surface with hyperbolic symmetry can be globally covered by compact hypersurfaces on which the mean curvature is constant and by compact hypersurfaces on which the area radius is constant. Results for the related cases of spherical and plane symmetry are reviewed and extended. The prospects of using the global time coordinates obtained in this way to investigate the global geometry of the spacetimes concerned are discusse
Existence of initial data satisfying the constraints for the spherically symmetric Einstein-Vlasov-Maxwell system
Using ODE techniques we prove the existence of large classes of initial data
satisfying the constraints for the spherically symmetric
Einstein-Vlasov-Maxwell system. These include data for which the ratio of total
charge to total mass is arbitrarily large.Comment: 12 page
Future non-linear stability for reflection symmetric solutions of the Einstein-Vlasov system of Bianchi types II and VI
Using the methods developed for the Bianchi I case we have shown that a
boostrap argument is also suitable to treat the future non-linear stability for
reflection symmetric solutions of the Einstein-Vlasov system of Bianchi types
II and VI. These solutions are asymptotic to the Collins-Stewart solution
with dust and the Ellis-MacCallum solution respectively. We have thus
generalized the results obtained by Rendall and Uggla in the case of locally
rotationally symmetric Bianchi II spacetimes to the reflection symmetric case.
However we needed to assume small data. For Bianchi VI there is no
analogous previous result.Comment: 30 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
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
Intermediate inflation and the slow-roll approximation
It is shown that spatially homogeneous solutions of the Einstein equations
coupled to a nonlinear scalar field and other matter exhibit accelerated
expansion at late times for a wide variety of potentials . These potentials
are strictly positive but tend to zero at infinity. They satisfy restrictions
on and related to the slow-roll approximation. These results
generalize Wald's theorem for spacetimes with positive cosmological constant to
those with accelerated expansion driven by potentials belonging to a large
class.Comment: 19 pages, results unchanged, additional backgroun
Global existence and asymptotic behaviour in the future for the Einstein-Vlasov system with positive cosmological constant
The behaviour of expanding cosmological models with collisionless matter and
a positive cosmological constant is analysed. It is shown that under the
assumption of plane or hyperbolic symmetry the area radius goes to infinity,
the spacetimes are future geodesically complete, and the expansion becomes
isotropic and exponential at late times. This proves a form of the cosmic no
hair theorem in this class of spacetimes
Simplified models of electromagnetic and gravitational radiation damping
In previous work the authors analysed the global properties of an approximate
model of radiation damping for charged particles. This work is put into context
and related to the original motivation of understanding approximations used in
the study of gravitational radiation damping. It is examined to what extent the
results obtained previously depend on the particular model chosen. Comparisons
are made with other models for gravitational and electromagnetic fields. The
relation of the kinetic model for which theorems were proved to certain
many-particle models with radiation damping is exhibited
- …