Spatially-homogeneous Vlasov-Einstein dynamics


Spatially-homogeneous Vlasov-Einstein dynamics

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dc.contributor.advisor Morrison, Philip J.
dc.creator Okabe, Takahide 2012-10-05T18:10:29Z 2012-10-05T18:10:29Z 2008-12 2012-10-05
dc.description.abstract The influence of matter described by the Vlasov equation, on the evolution of anisotropy in the spatially-homogeneous universes, called the Bianchi cosmologies, is studied. Due to the spatial-homogeneity, the Einstein equations for each Bianchi Type are reduced to a set of coupled ordinary differential equations, which has Hamiltonian form with the metric components being the canonical coordinates. In the vacuum Bianchi cosmologies, it is known that a curvature potential, which comes from the symmetries of the three-dimensional Lie groups, determines the basic properties of the evolution of anisotropy. In this work, matter potentials are constructed for Vlasov matter. They are obtained by first introducing a new matter action principle for the Vlasov equation, in terms of a conjugate pair of functions, and then enforcing the symmetry to obtain a reduction. This yields an expression for the matter potential in terms of the phase space density, which is further reduced by assuming cold streaming matter. Some vacuum Bianchi cosmologies and Type I with Vlasov matter are compared. It is shown that the Vlasov-matter potential for cold streaming matter results in qualitatively distinct dynamics from the well-known vacuum Bianchi cosmologies.
dc.format.medium electronic
dc.language.iso eng
dc.rights Copyright © is held by the author. Presentation of this material on the Libraries' web site by University Libraries, The University of Texas at Austin was made possible under a limited license grant from the author who has retained all copyrights in the works.
dc.subject.lcsh General relativity (Physics)--Mathematics
dc.subject.lcsh Cosmology--Mathematical models
dc.subject.lcsh Hamiltonian systems
dc.subject.lcsh Lie algebras
dc.subject.lcsh Lie groups
dc.subject.lcsh Anisotropy
dc.title Spatially-homogeneous Vlasov-Einstein dynamics
dc.description.department Physics
dc.type.genre Thesis
dc.type.material text Physics Physics The University of Texas at Austin Doctoral Doctor of Philosophy

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