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

Abstract

The dynamics of the Einstein-Vlasov equations for a class of cosmological models with four Killing vectors is discussed in the case of massive particles. It is shown that in all models analysed the solutions with massive particles are asymptotic to solutions with massless particles at early times. It is also shown that in Bianchi types I and II the solutions with massive particles are asymptotic to dust solutions at late times. That Bianchi type III models are also asymptotic to dust solutions at late times is consistent with our results but is not established by them.

21 pages, 2 figures

References in corpus (3)

• Isotropic cosmological singularities 2: The Einstein-Vlasov system
• Dynamics of spatially homogeneous solutions of the Einstein-Vlasov equations which are locally rotationally symmetric
• Isotropic cosmological singularities 3: The Cauchy problem for the inhomogeneous conformal Einstein-Vlasov equations

Cited by in corpus (20)

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• Dynamics of the spatially homogeneous Bianchi type I Einstein-Vlasov equations
• Fuchsian analysis of S^2xS^1 and S^3 Gowdy spacetimes
• Global Existence of Solutions for the Einstein-Boltzmann System in a Bianchi Type I Space-Time
• The Einstein-Vlasov sytem/Kinetic theory
• Isotropization of non-diagonal Bianchi I spacetimes with collisionless matter at late times assuming small data
• On the oscillations and future asymptotics of locally rotationally symmetric Bianchi type III cosmologies with a massive scalar field
• Averaging with a time-dependent perturbation parameter
• 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
• Structure of solutions near the initial singularity for the surface-symmetric Einstein-Vlasov system
• Dynamics of locally rotationally symmetric Bianchi type VIII cosmologies with anisotropic matter
• Future attractors of Bianchi types II and V cosmologies with massless Vlasov matter
• Late-time behaviour of the Einstein-Vlasov system with Bianchi I symmetry