Related papers: Global dynamics of the mixmaster model
The well-known Bielinski-Khalatnikov-Lifshitz (BKL) scenario for the universe near the cosmological singularity is supplemented with a few exact results following from the BKL asymptotic of the Einstein equations: (1) The cosmological…
We use expansion-normalised variables to investigate the Bianchi type VII$_0$ model with a tilted $\gamma$-law perfect fluid. We emphasize the late-time asymptotic dynamical behaviour of the models and determine their asymptotic states.…
The Bianchi type $\mathrm{VI}_{-1/9}$, $\mathrm{VIII}$ and $\mathrm{IX}$ vacuum models all have 4-dimensional Hubble-normalized state spaces and are expected to have a generic initial oscillatory singularity, but the invariant boundary sets…
In classical general relativity, the generic approach to the initial singularity is usually understood in terms of the BKL scenario. In this scenario, along with the Bianchi IX model, the exact, singular, Kasner solution of vacuum Bianchi I…
We investigate the behaviour on approach to the initial singularity in higher-order extensions of general relativity by finding exact cosmological solutions for a wide class of models in which the Lagrangian is allowed to depend nonlinearly…
In one-loop string effective action, we study a generality of non-singular cosmological solutions found in the isotropic and homogeneous case. We discuss Bianchi I and IX type spacetimes. We find that nonsingular solutions still exist in…
We show that an ansatz for $1+3+n$ dimensional static spacetime with spherical symmetry in three dimensions and Euclidean symmetry in $n$ dimensions, parametrized by only one function of radial coordinate, leads to a limited set of vacuum…
Contrary to the general belief, there has recently been quite a few examples of unitary evolution of quantum cosmological models. The present work gives more examples, namely Bianchi type VI and type II. These examples are important as they…
In this paper we give, for the first time, a complete description of the late-time evolution of non-tilted spatially homogeneous cosmologies of Bianchi type VIII. The source is assumed to be a perfect fluid with equation of state $p =…
We find instanton/cosmological solutions with biaxial Bianchi-IX symmetry, involving non-trivial spatial dependence of the $\bbbc P^{1}$- and $\bbbc P^{2}$-sigma-models coupled to gravity. Such manifolds arise in N=1, $d=4$ supergravity…
Global existence results in the past time direction of cosmological models with collisionless matter and a massless scalar field are presented. It is shown that the singularity is crushing and that the Kretschmann scalar diverges uniformly…
We consider some aspects of the global evolution problem of Hamiltonian homogeneous, anisotropic cosmologies derived from a purely quadratic action functional of the scalar curvature. We show that models can isotropize in the positive…
Bianchi VIII vacuum solutions to Einstein's equations are causally geodesically complete to the future, given an appropriate time orientation, and the objective of this article is to analyze the asymptotic behaviour of solutions in this…
We study the dynamics of the vacuum Bianchi IX model with timelike singularity and compare it with the dynamics of the Bianchi IX model with cosmological singularity. We show that differences in the signs of some terms in the set of…
We consider solutions of the Einstein vacuum equations which arise from smooth initial data on a hypersurface slightly inside a dynamical black hole settling down to a subextremal Kerr black hole, and satisfying a precise non-linear Price's…
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…
We study the homogeneous and anisotropic evolution of Bianchi type-I spacetime driven by perfect fluid with shear viscosity. We obtain exact solutions by considering the simplest form of the equation of state wherein the pressure and the…
The mathematical structure of higher-dimensional physical phase spaces of the nondiagonal Bianchi IX model is analyzed in the neighborhood of the cosmological singularity by using dynamical system methods. Critical points of the Hamiltonian…
In this work, we study some physical aspects of unitary evolution of Bianchi-I model. In particular, we study the behavior of the volume and the scale factor as a function of time for the Bianchi-I universe with ultra-relativistic fluid…
We consider the Bianchi I geometry coupled to several species of comoving barotropic perfect fluids with a linear equation of state in the context of general relativity. The solution of the dynamics can be reduced to a quadrature, which can…