Dynamics of spatially homogeneous solutions of the Einstein-Vlasov equations which are locally rotationally symmetric

Abstract

The dynamics of a class of cosmological models with collisionless matter and four Killing vectors is studied in detail and compared with that of corresponding perfect fluid models. In many cases it is possible to identify asymptotic states of the spacetimes near the singularity or in a phase of unlimited expansion. Bianchi type II models show oscillatory behaviour near the initial singularity which is, however, simpler than that of the mixmaster model.

27 pages, 3 figures, LaTeX

Cited by in corpus (25)

• The Einstein-Vlasov System/Kinetic Theory
• Cosmological models and centre manifold theory
• The Einstein-Vlasov system/Kinetic theory
• Theorems on existence and global dynamics for the Einstein equations
• Dynamics of spatially homogeneous locally rotationally symmetric solutions of the Einstein-Vlasov equations
• Manufacture of Gowdy spacetimes with spikes
• Dynamics of magnetic Bianchi VI_0 cosmologies
• Bianchi Cosmologies with Anisotropic Matter: Locally Rotationally Symmetric Models
• Dynamics of the spatially homogeneous Bianchi type I Einstein-Vlasov equations
• Newtonian Stellar Models
• Fuchsian analysis of S^2xS^1 and S^3 Gowdy spacetimes
• The Einstein-Vlasov sytem/Kinetic theory
• Isotropization of non-diagonal Bianchi I spacetimes with collisionless matter at late times assuming small data
• A class of plane symmetric perfect-fluid cosmologies with a Kasner-like singularity
• Local and global existence theorems for the Einstein equations
• Monotonic functions in Bianchi models: Why they exist and how to find them
• Isotropization of Slowly Expanding Spacetimes
• Future non-linear stability for reflection symmetric solutions of the Einstein-Vlasov system of Bianchi types II and VI${}_0$
• Kantowski-Sachs cosmology with Vlasov matter
• Future attractors of Bianchi types II and V cosmologies with massless Vlasov matter
• On the future of solutions to the massless Einstein-Vlasov system in a Bianchi I cosmology
• Cosmological models and stability
• Asymptotic behavior of a matter filled universe with exotic topology
• Einstein flow with matter sources: stability and convergence
• Late-time behaviour of the Einstein-Vlasov system with Bianchi I symmetry