Related papers: Cosmological Billiards
This article is devoted to a study of the asymptotic dynamics of generic solutions of the Einstein vacuum equations toward a generic spacelike singularity. Starting from fundamental assumptions about the nature of generic spacelike…
The structure of the general, inhomogeneous solution of (bosonic) Einstein-matter systems in the vicinity of a cosmological singularity is considered. We review the proof (based on ideas of Belinskii-Khalatnikov-Lifshitz and technically…
The structure of the general, inhomogeneous solution of (bosonic) Einstein-matter systems in the vicinity of a cosmological singularity is considered. We review the proof (based on ideas of Belinskii-Khalatnikov-Lifshitz and technically…
Multidimensional cosmological-type model with n Einstein factor spaces in the theory with l scalar fields and multiple exponential potential is considered. The dynamics of the model near the singularity is reduced to a billiard on the…
Multidimensional model describing the cosmological evolution of n Einstein spaces in the theory with l scalar fields and forms is considered. When electro-magnetic composite p-brane ansatz is adopted, and certain restrictions on the…
The multidimensional cosmological model describing the evolution of $n$ Einstein spaces in the presence of multicomponent perfect fluid is considered. When certain restrictions on the parameters of the model are imposed, the dynamics of the…
A short overview of the billiard approach for cosmological-type models with n Einstein factor-spaces is presented. We start with the billiard representation for pseudo-Euclidean Toda-like systems of cosmological origin. Then we consider…
Belinski, Khalatnikov and Lifshitz (BKL) pioneered the study of the statistical properties of the never-ending oscillatory behavior (among successive Kasner epochs) of the geometry near a space-like singularity. We show how the use of a…
The degenerate Lagrangian system describing a lot of cosmological models is considered. When certain restrictions on the parameters of the model are imposed, the dynamics of the model near the "singularity" is reduced to a billiard on the…
The existence of a singularity by definition implies a preferred scale--the affine parameter distance from/to the singularity of a causal geodesic that is used to define it. However, this variable scale is also captured by the expansion…
In this paper, we analyse the Einstein and Einstein-Maxwell billiards for all spatially homogeneous cosmological models corresponding to 3 and 4 dimensional real unimodular Lie algebras and provide the list of those models which are chaotic…
The pseudo-Euclidean Toda-like system of cosmological origin is considered. When certain restrictions on the parameters of the model are imposed, the dynamics of the model near the ``singularity'' is reduced to a billiard on the…
In recent papers, it has been shown that (i) the dynamics of theories involving gravity can be described, in the vicinity of a spacelike singularity, as a billiard motion in a region of hyperbolic space bounded by hyperplanes; and (ii) that…
We study the quantum fermionic billiard defined by the dynamics of a quantized supersymmetric squashed three-sphere (Bianchi IX cosmological model within D=4 simple supergravity). The quantization of the homogeneous gravitino field leads to…
D=11 Supergravity near a space-like singularity admits a cosmological billiard description based on the hyperbolic Kac-Moody group E10. The quantization of this system via the supersymmetry constraint is shown to lead to wavefunctions…
The problem of construction of a general ihomogeneous solution of $D$-dimensional Einstein equations in the vicinity of a cosmological singularity is considered. It is shown that near the singularity a local behavior of metric functions is…
We analyze the dynamics of the Mixmaster Universe on the base of a standard Arnowitt-Deser-Misner Hamiltonian approach showing how its asymptotic evolution to the cosmological singularity is isomorphic to a billiard on the Lobachevsky…
Spatially homogeneous cosmological models reduce to Hamiltonian systems in a low dimensional Minkowskian space moving on the total energy shell $H=0$. Close to the initial singularity some models (those of Bianchi type VIII and IX) can be…
Close to a spacelike singularity, pure gravity and supergravity in four to eleven spacetime dimensions admit a cosmological billiard description based on hyperbolic Kac-Moody groups. We investigate the quantum cosmological billiards of…
We review the intimate connection between (super-)gravity close to a spacelike singularity (the "BKL-limit") and the theory of Lorentzian Kac-Moody algebras. We show that in this limit the gravitational theory can be reformulated in terms…