Oscillations toward the Singularity of Locally Rotationally Symmetric Bianchi Type IX Cosmological Models with Vlasov Matter
- Author(s)
- Simone Calogero, Johannes Markus Heinzle
- Abstract
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(s)
- Gravitational Physics
- External organisation(s)
- Universidad de Granada
- Journal
- SIAM Journal on Applied Dynamical Systems
- Volume
- 9
- Pages
- 1244-1262
- No. of pages
- 19
- ISSN
- 1536-0040
- DOI
- https://doi.org/10.1137/100782590
- Publication date
- 2010
- Peer reviewed
- Yes
- Austrian Fields of Science 2012
- 103036 Theoretical physics, 103028 Theory of relativity, 103019 Mathematical physics
- Portal url
- https://ucrisportal.univie.ac.at/en/publications/oscillations-toward-the-singularity-of-locally-rotationally-symmetric-bianchi-type-ix-cosmological-models-with-vlasov-matter(3d319e08-7fff-4bda-a11f-64b8efabbb4f).html