448 research outputs found
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
Dynamics of spatially homogeneous solutions of the Einstein-Vlasov equations which are locally rotationally symmetric
Manufacture of Gowdy spacetimes with spikes
In numerical studies of Gowdy spacetimes evidence has been found for the
development of localized features (spikes) involving large gradients near the
singularity. The rigorous mathematical results available up to now did not
cover this kind of situation. In this work we show the existence of large
classes of Gowdy spacetimes exhibiting features of the kind discovered
numerically. These spacetimes are constructed by applying certain
transformations to previously known spacetimes without spikes. It is possible
to control the behaviour of the Kretschmann scalar near the singularity in
detail. This curvature invariant is found to blow up in a way which is
non-uniform near the spike in some cases. When this happens it demonstrates
that the spike is a geometrically invariant feature and not an artefact of the
choice of variables used to parametrize the metric. We also identify another
class of spikes which are artefacts. The spikes produced by our method are
compared with the results of numerical and heuristic analyses of the same
situation.Comment: 25 page
Mixmaster Behavior in Inhomogeneous Cosmological Spacetimes
Numerical investigation of a class of inhomogeneous cosmological spacetimes
shows evidence that at a generic point in space the evolution toward the
initial singularity is asymptotically that of a spatially homogeneous spacetime
with Mixmaster behavior. This supports a long-standing conjecture due to
Belinskii et al. on the nature of the generic singularity in Einstein's
equations.Comment: 4 pages plus 4 figures. A sentence has been deleted. Accepted for
publication in PR
Dynamics of spatially homogeneous solutions of the Einstein-Vlasov equations which are locally rotationally symmetric
The dynamics of a class of cosmological models with collisionless matter and
four Killing vectors is studied in detail and compared with that of
corresponding perfect fluid models. In many cases it is possible to identify
asymptotic states of the spacetimes near the singularity or in a phase of
unlimited expansion. Bianchi type II models show oscillatory behaviour near the
initial singularity which is, however, simpler than that of the mixmaster
model.Comment: 27 pages, 3 figures, LaTe
Curvature blow up in Bianchi VIII and IX vacuum spacetimes
The maximal globally hyperbolic development of non-Taub-NUT Bianchi IX vacuum
initial data and of non-NUT Bianchi VIII vacuum initial data is C2
inextendible. Furthermore, a curvature invariant is unbounded in the incomplete
directions of inextendible causal geodesics.Comment: 20 pages, no figures. Submitted to Classical and Quantum Gravit
Accelerated cosmological expansion due to a scalar field whose potential has a positive lower bound
In many cases a nonlinear scalar field with potential can lead to
accelerated expansion in cosmological models. This paper contains mathematical
results on this subject for homogeneous spacetimes. It is shown that, under the
assumption that has a strictly positive minimum, Wald's theorem on
spacetimes with positive cosmological constant can be generalized to a wide
class of potentials. In some cases detailed information on late-time
asymptotics is obtained. Results on the behaviour in the past time direction
are also presented.Comment: 16 page
The Newtonian Limit for Asymptotically Flat Solutions of the Vlasov-Einstein System
It is shown that there exist families of asymptotically flat solutions of the
Einstein equations coupled to the Vlasov equation describing a collisionless
gas which have a Newtonian limit. These are sufficiently general to confirm
that for this matter model as many families of this type exist as would be
expected on the basis of physical intuition. A central role in the proof is
played by energy estimates in unweighted Sobolev spaces for a wave equation
satisfied by the second fundamental form of a maximal foliation.Comment: 24 pages, plain TE
Critical collapse of collisionless matter - a numerical investigation
In recent years the threshold of black hole formation in spherically
symmetric gravitational collapse has been studied for a variety of matter
models. In this paper the corresponding issue is investigated for a matter
model significantly different from those considered so far in this context. We
study the transition from dispersion to black hole formation in the collapse of
collisionless matter when the initial data is scaled. This is done by means of
a numerical code similar to those commonly used in plasma physics. The result
is that for the initial data for which the solutions were computed, most of the
matter falls into the black hole whenever a black hole is formed. This results
in a discontinuity in the mass of the black hole at the onset of black hole
formation.Comment: 22 pages, LaTeX, 7 figures (ps-files, automatically included using
psfig
Cauchy horizons in Gowdy space times
We analyse exhaustively the structure of \emph{non-degenerate} Cauchy
horizons in Gowdy space-times, and we establish existence of a large class of
non-polarized Gowdy space-times with such horizons.
Added in proof: Our results here, together with deep new results of H.
Ringstr\"om (talk at the Miami Waves conference, January 2004), establish
strong cosmic censorship in (toroidal) Gowdy space-times.Comment: 25 pages Latex. Further information at http://grtensor.org/gowdy
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