5 research outputs found
The Speciality Index as invariant indicator in the BKL Mixmaster Dynamics
The speciality index, which has been mainly used in Numerical Relativity for
studying gravitational waves phenomena as an indicator of the special or
non-special Petrov type character of a spacetime, is applied here in the
context of Mixmaster cosmology, using the Belinski-Khalatnikov-Lifshitz map.
Possible applications for the associated chaotic dynamics are discussed
Quasi-isotropic cycles and non-singular bounces in a Mixmaster cosmology
A Bianchi IX Mixmaster spacetime is the most general spatially homogeneous
solution of Einstein's equations and it can represent the space-averaged
Universe. We introduce two novel mechanisms resulting in a Mixmaster Universe
with non-singular bounces which are quasi-isotropic. A fluid with a non-linear
equation of state allows non-singular bounces. Using negative anisotropic
stresses successfully isotropises this Universe and mitigates the well known
Mixmaster chaotic behaviour. Thus the Universe can be an eternal Mixmaster,
going through an infinite series of different cycles separated by bounces, with
a sizable fraction of cycles isotropic enough to be well approximated by a
standard Friedmann-Lema\^itre-Robertson-Walker model from the radiation era
onward.Comment: 5 pages, 4 figure
Spike Oscillations
According to Belinskii, Khalatnikov and Lifshitz (BKL), a generic spacelike
singularity is characterized by asymptotic locality: Asymptotically, toward the
singularity, each spatial point evolves independently from its neighbors, in an
oscillatory manner that is represented by a sequence of Bianchi type I and II
vacuum models. Recent investigations support a modified conjecture: The
formation of spatial structures (`spikes') breaks asymptotic locality. The
complete description of a generic spacelike singularity involves spike
oscillations, which are described by sequences of Bianchi type I and certain
inhomogeneous vacuum models. In this paper we describe how BKL and spike
oscillations arise from concatenations of exact solutions in a
Hubble-normalized state space setting, suggesting the existence of hidden
symmetries and showing that the results of BKL are part of a greater picture.Comment: 38 pages, 14 figure
Mixmaster: Fact and Belief
We consider the dynamics towards the initial singularity of Bianchi type IX
vacuum and orthogonal perfect fluid models with a linear equation of state.
Surprisingly few facts are known about the `Mixmaster' dynamics of these
models, while at the same time most of the commonly held beliefs are rather
vague. In this paper, we use Mixmaster facts as a base to build an
infrastructure that makes it possible to sharpen the main Mixmaster beliefs. We
formulate explicit conjectures concerning (i) the past asymptotic states of
type IX solutions and (ii) the relevance of the Mixmaster/Kasner map for
generic past asymptotic dynamics. The evidence for the conjectures is based on
a study of the stochastic properties of this map in conjunction with dynamical
systems techniques. We use a dynamical systems formulation, since this approach
has so far been the only successful path to obtain theorems, but we also make
comparisons with the `metric' and Hamiltonian `billiard' approaches.Comment: 34 pages, 10 figure