268 research outputs found
An exact smooth Gowdy-symmetric generalized Taub-NUT solution
In a recent paper (Beyer and Hennig, 2012 [9]), we have introduced a class of
inhomogeneous cosmological models: the smooth Gowdy-symmetric generalized
Taub-NUT solutions. Here we derive a three-parametric family of exact solutions
within this class, which contains the two-parametric Taub solution as a special
case. We also study properties of this solution. In particular, we show that
for a special choice of the parameters, the spacetime contains a curvature
singularity with directional behaviour that can be interpreted as a "true
spike" in analogy to previously known Gowdy symmetric solutions with spatial
T3-topology. For other parameter choices, the maximal globally hyperbolic
region is singularity-free, but may contain "false spikes".Comment: 39 pages, 3 figure
Second-order hyperbolic Fuchsian systems. Gowdy spacetimes and the Fuchsian numerical algorithm
This is the second part of a series devoted to the singular initial value
problem for second-order hyperbolic Fuchsian systems. In the first part, we
defined and investigated this general class of systems, and we established a
well-posedness theory in weighted Sobolev spaces. This theory is applied here
to the vacuum Einstein equations for Gowdy spacetimes admitting, by definition,
two Killing fields satisfying certain geometric conditions. We recover, by more
direct and simpler arguments, the well-posedness results established earlier by
Rendall and collaborators. In addition, in this paper we introduce a natural
approximation scheme, which we refer to as the Fuchsian numerical algorithm and
is directly motivated by our general theory. This algorithm provides highly
accurate, numerical approximations of the solution to the singular initial
value problem. In particular, for the class of Gowdy spacetimes under
consideration, various numerical experiments are presented which show the
interest and efficiency of the proposed method. Finally, as an application, we
numerically construct Gowdy spacetimes containing a smooth, incomplete,
non-compact Cauchy horizon.Comment: 22 pages. A shortened version is included in: F. Beyer and P.G.
LeFloch, Second-order hyperbolic Fuchsian systems and applications, Class.
Quantum Grav. 27 (2010), 24501
Criticality of inhomogeneous Nariai-like cosmological models
In this paper, we construct and study solutions of Einstein's equations in
vacuum with a positive cosmological constant which can be considered as
inhomogeneous generalizations of the Nariai cosmological model. Similar to this
Nariai spacetime, our solutions are at the borderline between gravitational
collapse and de-Sitter-like exponential expansion. Our studies focus in
particular on the intriguing oscillatory dynamics which we discover. Our
investigations are carried out both analytically (using heuristic mode analysis
arguments) and numerically (using the numerical infrastructure recently
introduced by us).Comment: 34 pages, 17 figure
- …