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A study of integrability conditions for irrotational dust spacetimes
Bibliography: pages 139-145.
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| Other Authors: | |
| Format: | Thesis |
| Language: | English |
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Department of Mathematics and Applied Mathematics
2016
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| _version_ | 1867613330804310016 |
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| access_status_str | Open Access |
| author | Lesame, William Mphepeng |
| author2 | Ellis, George F R |
| author_browse | Ellis, George F R Lesame, William Mphepeng |
| author_facet | Ellis, George F R Lesame, William Mphepeng |
| author_sort | Lesame, William Mphepeng |
| collection | Thesis |
| description | Bibliography: pages 139-145. |
| format | Thesis |
| id | oai:open.uct.ac.za:11427/21328 |
| institution | University of Cape Town (South Africa) |
| language | eng |
| last_indexed | 2026-06-10T12:34:25.395Z |
| 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:11427/21328 A study of integrability conditions for irrotational dust spacetimes Lesame, William Mphepeng Ellis, George F R Mathematics and Applied Mathematics Bibliography: pages 139-145. This thesis examines consistency conditions for fluid solutions of the field equations of general relativity. The exact non-linear dynamic equations for a generic irrotational dust spacetime are consistent. To analyse conditions characterizing pure gravity waves, linearization instability in general relativity and consistency of the so-called "silent universes", further exact conditions are imposed locally on irrotational dust. These are classified into Class II conditions, which change evolution equations into constraint equations, and Class I and III conditions, which do not doso-rather they add a new constraint, leaving the propagation equations unchanged in form. Class I conditions are imposed on terms in the constraint equations, while Class II and III conditions are imposed on terms in the evolution equations. In the Class I case it is shown that for irrotational dust space times the divergence-free magnetic Weyl tensor and the divergence-free electric Weyl tensor (necessary conditions for gravity waves interacting with matter), both imply integrability conditions in the exact non-linear case. The integrability conditions for the divergence-free magnetic Weyl tensor are identically satisfied in the linearized perturbation case, but are non-trivial in the exact non-linear case. This leads to a linearization instability in these models. The integrability conditions for the divergence-free electric Weyltensor are non-trivial in both the linear and non-linear cases. The Class II case focuses on irrotational silent cosmological dust models characterized by vanishing magnetic Weyl tensor and vanishing electric Weyl tensor. In both these models there exist a series of integrability conditions that need to be satisfied. Integrability conditions for the zero magnetic Weyl tensor condition hold identically for linearized case, but are non-trivial in the exact non-linear case. Thus there is also a linearization instability. The zero electric Weyl tensor condition leads to a chain of non-trivial integrability conditions in both the linear and non-linear cases. Because of the complexity of the integrability conditions, it is highly unlikely that there is a large class of models in both the silent zero magnetic Weyl tensor case and the silent zero electric Weyl tensor case. 2016-08-18T13:51:02Z 2016-08-18T13:51:02Z 1998 Doctoral Thesis Doctoral PhD http://hdl.handle.net/11427/21328 eng application/pdf Department of Mathematics and Applied Mathematics Faculty of Science University of Cape Town |
| spellingShingle | Mathematics and Applied Mathematics Lesame, William Mphepeng A study of integrability conditions for irrotational dust spacetimes |
| thesis_degree_str | Doctoral |
| title | A study of integrability conditions for irrotational dust spacetimes |
| title_full | A study of integrability conditions for irrotational dust spacetimes |
| title_fullStr | A study of integrability conditions for irrotational dust spacetimes |
| title_full_unstemmed | A study of integrability conditions for irrotational dust spacetimes |
| title_short | A study of integrability conditions for irrotational dust spacetimes |
| title_sort | study of integrability conditions for irrotational dust spacetimes |
| topic | Mathematics and Applied Mathematics |
| url | http://hdl.handle.net/11427/21328 |
| work_keys_str_mv | AT lesamewilliammphepeng astudyofintegrabilityconditionsforirrotationaldustspacetimes AT lesamewilliammphepeng studyofintegrabilityconditionsforirrotationaldustspacetimes |