Related papers: On a proof of the collapse conjecture for a diagon…
We consider the asymptotic behaviour of spatially homogeneous spacetimes of Bianchi type IX close to the singularity (we also consider some of the other Bianchi types, e. g. Bianchi VIII in the stiff fluid case). The matter content is…
We consider the dynamics towards the initial singularity of Bianchi type IX vacuum and orthogonal perfect fluid models with a linear equation of state. The `Bianchi type IX attractor theorem' states that the past asymptotic behavior of…
The Bianchi IX cosmological model (through Bianchi I and II) is analyzed in the framework of a generalized uncertainty principle. In particular, the anisotropies of the Universe are described by a deformed Heisenberg algebra. Three main…
It is shown that all contracting, spatially homogeneous, orthogonal Bianchi cosmologies that are sourced by an ultra-stiff fluid with an arbitrary and, in general, varying equation of state asymptote to the spatially flat and isotropic…
We investigate the integrability of an anisotropic universe with matter and cosmological constant formulated as Bianchi IX models. The presence of the cosmological constant causes the existence of a critical point in the finite part of the…
In order to investigate if the anisotropy of the spacetime may induce future singularities at a finite value of the cosmic time on the evolution of cosmological models, we study vacuum and non-vacuum Bianchi type I spacetimes exhibiting…
In this paper, we prove that the 5-dimensional Schwarzschild-Tangherlini solution of the Einstein vacuum equations is orbitally stable (in the fully non-linear theory) with respect to vacuum perturbations of initial data preserving triaxial…
We investigate a model of gravitational collapse of matter inhomogeneities where the latter are modelled as Bianchi type IX (BIX) spacetimes. We found that this model contains, as limiting cases, both the standard spherical collapse model…
Within the scope of anisotropic non-diagonal Bianchi type-II, VIII and IX spacetime it is shown that the off-diagonal components of the corresponding metric impose severe restrictions on the components of the energy momentum tensor in…
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…
Bianchi models are posited by the BKL picture to be essential building blocks towards an understanding of generic cosmological singularities. We study the behaviour of spatially homogeneous anisotropic vacuum spacetimes of Bianchi type VIII…
The asymptotic behaviour of vacuum Bianchi models of class A near the initial singularity is studied, in an effort to confirm the standard picture arising from heuristic and numerical approaches by mathematical proofs. It is shown that for…
Continuing previous work, we show the existence of stable, anisotropic future attractors in Bianchi invariant sets with a $p$-form field ($p\,\in\,\{1,3\}$) and a perfect fluid. In particular, we consider the not previously investigated…
We consider the vacuum gravitational collapse for cohomogeneity-two solutions of the nine dimensional Einstein equations. Using combined numerical and analytical methods we give evidence that within this model the Schwarzschild-Tangherlini…
We study tilted perfect fluid cosmological models with a constant equation of state parameter in spatially homogeneous models of Bianchi type VI_h using dynamical systems methods and numerical experimentation, with an emphasis on their…
We show several kinematical properties that are intrinsic to the Bianchi models with compact spatial sections. Especially, with spacelike hypersurfaces being closed, (A) no anisotropic expansion is allowed for Bianchi type V and…
In this paper we study oscillatory Bianchi models of class A and are able to show that for admissible periodic heteroclinic chains in Bianchi IX there exisist $C^{1}$- stable - manifolds of orbits that follow these chains towards the big…
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…
We study numerically the solutions to the effective equations of Bianchi IX spacetimes within Loop Quantum Cosmology. We consider Bianchi IX models with and without inverse triad corrections whose matter content is a scalar field without…
The gravitational collapse of an infinite cylindrical thin shell of generic matter in an otherwise empty spacetime is considered. We show that geometries admitting two hypersurface orthogonal Killing vectors cannot contain trapped surfaces…