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Hamiltonian Dynamics of Spatially-Homogeneous Vlasov-Einstein Systems | | Takahide Okabe
; P. J. Morrison
; J. E. Friedrichsen III
; L. C. Shepley
; | | Date: |
23 Jun 2011 | | Abstract: | We introduce a new matter action principle, with a wide range of
applicability, for the Vlasov equation in terms of a conjugate pair of
functions. Here we apply this action principle to the study of matter in
Bianchi cosmological models in general relativity. The Bianchi models are
spatially-homogeneous solutions to the Einstein field equations, classified by
the three-dimensional Lie algebra that describes the symmetry group of the
model. The Einstein equations for these models reduce to a set of coupled
ordinary differential equations. The class A Bianchi models admit a Hamiltonian
formulation in which the components of the metric tensor and their time
derivatives yield the canonical coordinates. The evolution of anisotropy in the
vacuum Bianchi models is determined by a potential due to the curvature of the
model, according to its symmetry. For illustrative purposes, we examine the
evolution of anisotropy in models with Vlasov matter. The Vlasov content is
further simplified by the assumption of cold, counter-streaming matter, a kind
of matter that is far from thermal equilibrium and is not describable by an
ordinary fluid model nor other more simplistic matter models. Qualitative
differences and similarities are found in the dynamics of certain vacuum class
A Bianchi models and Bianchi Type I models with cold, counter-streaming Vlasov
matter potentials analogous to the curvature potentials of corresponding vacuum
models. | | Source: | arXiv, 1106.4807 | | Services: | Forum | Review | PDF | Favorites | |
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