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Exact non-equilibrium solutions of the Einstein-Boltzmann equations
Includes bibliographical references.
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| Main Author: | |
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| Other Authors: | |
| Format: | Thesis |
| Language: | English |
| Published: |
Department of Mathematics and Applied Mathematics
2016
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| _version_ | 1867613230548910080 |
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| access_status_str | Open Access |
| author | Wolvaardt, F P |
| author2 | Maartens, Roy |
| author_browse | Maartens, Roy Wolvaardt, F P |
| author_facet | Maartens, Roy Wolvaardt, F P |
| author_sort | Wolvaardt, F P |
| collection | Thesis |
| description | Includes bibliographical references. |
| format | Thesis |
| id | oai:open.uct.ac.za:11427/17445 |
| institution | University of Cape Town (South Africa) |
| language | eng |
| last_indexed | 2026-06-10T12:32:50.328Z |
| license_str | Not specified — see source repository |
| provenance_str_mv | Harvested via OAI-PMH from UCTD — University of Cape Town Open Access Repository |
| publishDate | 2016 |
| publishDateRange | 2016 |
| publishDateSort | 2016 |
| publisher | Department of Mathematics and Applied Mathematics |
| publisherStr | Department of Mathematics and Applied Mathematics |
| record_format | dspace |
| source_str | UCTD — University of Cape Town Open Access Repository |
| spelling | oai:open.uct.ac.za:11427/17445 Exact non-equilibrium solutions of the Einstein-Boltzmann equations Wolvaardt, F P Maartens, Roy Applied Mathematics Includes bibliographical references. In this thesis we use the exact solution of the Boltzmann equation, with a relaxation-time model of collisions, to find solutions of the Einstein-Boltzmann system of equations. A covariant harmonic decomposition of the distribution function is used to obtain exact results. The conditions imposed by the conservation of particle number and energy-momentum, and by the H-theorem are determined. The properties of exact truncated Boltzmann solutions with first and second order anisotropies are investigated. Exact entropy results are obtained for the solution with first order anisotropy, and the solution with second order anisotropy is shown to obey exact thermodynamics laws. The Einstein-Boltzmann equations with relaxation-time model of collisions are solved in FRW and Bianchi I spacetime. In FRW spacetime, a general anisotropic solution and an isotropic solution are obtained. The non-equilibrium anisotropic solution with arbitrary isotropic relaxation function has vanishing particle flux and an equilibrium energy-momentum tensor. Specific forms of the relaxation function permit tilted solutions and solutions with non-zero bulk viscosity. Exact entropy results are derived for the isotropic solution showing that the H-theorem is satisfied. The non-equilibrium isotropic solution has vanishing non-equilibrium pressures and fluxes. The FRW and Bianchi I solutions are used to demonstrate the generation of anisotropy in FRW cosmologies. A relaxation length model of collisions is introduced. This model is used to obtain solutions of the Einstein-Boltzmann equations in static spherically symmetric spacetime. In this static model, anisotropic pressure comes from the bulk viscosity. 2016-03-04T16:34:25Z 2016-03-04T16:34:25Z 1994 Doctoral Thesis Doctoral PhD http://hdl.handle.net/11427/17445 eng application/pdf Department of Mathematics and Applied Mathematics Faculty of Science University of Cape Town |
| spellingShingle | Applied Mathematics Wolvaardt, F P Exact non-equilibrium solutions of the Einstein-Boltzmann equations |
| thesis_degree_str | Doctoral |
| title | Exact non-equilibrium solutions of the Einstein-Boltzmann equations |
| title_full | Exact non-equilibrium solutions of the Einstein-Boltzmann equations |
| title_fullStr | Exact non-equilibrium solutions of the Einstein-Boltzmann equations |
| title_full_unstemmed | Exact non-equilibrium solutions of the Einstein-Boltzmann equations |
| title_short | Exact non-equilibrium solutions of the Einstein-Boltzmann equations |
| title_sort | exact non equilibrium solutions of the einstein boltzmann equations |
| topic | Applied Mathematics |
| url | http://hdl.handle.net/11427/17445 |
| work_keys_str_mv | AT wolvaardtfp exactnonequilibriumsolutionsoftheeinsteinboltzmannequations |