Oscillations toward the Singularity of Locally Rotationally Symmetric Bianchi Type IX Cosmological Models with Vlasov Matter

Autor(en)

Simone Calogero, Johannes Markus Heinzle

Abstrakt

We analyze the dynamics of a class of cosmological solutions of the Einstein–Vlasov equations. These equations describe an ensemble of collisionless particles (which represent galaxies or clusters of galaxies) that interact gravitatively through Einstein's equations of general relativity. The cosmological models we consider are spatially homogeneous, of Bianchi type IX, and locally rotationally symmetric (LRS). We prove that generic solutions exhibit an oscillatory behavior close to the singularities (the “big bang” in the past and the “big crunch” in the future); this is in contrast to the behavior of Einstein-vacuum or Einstein–Euler solutions. To establish this result we make use of dynamical systems theory; we introduce dimensionless dynamical variables that are defined on a compact state space. In this formulation the oscillatory behavior of generic solutions is represented by the existence of heteroclinic cycles on the boundary of the state space.

Organisation(en)

Gravitationsphysik

Externe Organisation(en)

Universidad de Granada

Journal

SIAM Journal on Applied Dynamical Systems

Band

9

Seiten

1244-1262

Anzahl der Seiten

19

ISSN

1536-0040

DOI

https://doi.org/10.1137/100782590

Publikationsdatum

2010

Peer-reviewed

Ja

ÖFOS 2012

103036 Theoretische Physik, 103028 Relativitätstheorie, 103019 Mathematische Physik

Link zum Portal

https://ucrisportal.univie.ac.at/de/publications/3d319e08-7fff-4bda-a11f-64b8efabbb4f