A study of integrability conditions for irrotational dust spacetimes

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dc.contributor.advisorEllis, George F Ren_ZA
dc.contributor.authorLesame, William Mphepengen_ZA
dc.date.accessioned2016-08-18T13:51:02Z
dc.date.available2016-08-18T13:51:02Z
dc.date.issued1998en_ZA
dc.descriptionBibliography: pages 139-145.en_ZA
dc.description.abstractThis 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.en_ZA
dc.identifier.apacitationLesame, W. M. (1998). <i>A study of integrability conditions for irrotational dust spacetimes</i>. (Thesis). University of Cape Town ,Faculty of Science ,Department of Mathematics and Applied Mathematics. Retrieved from http://hdl.handle.net/11427/21328en_ZA
dc.identifier.chicagocitationLesame, William Mphepeng. <i>"A study of integrability conditions for irrotational dust spacetimes."</i> Thesis., University of Cape Town ,Faculty of Science ,Department of Mathematics and Applied Mathematics, 1998. http://hdl.handle.net/11427/21328en_ZA
dc.identifier.citationLesame, W. 1998. A study of integrability conditions for irrotational dust spacetimes. University of Cape Town.en_ZA
dc.identifier.ris TY - Thesis / Dissertation AU - Lesame, William Mphepeng AB - 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. DA - 1998 DB - OpenUCT DP - University of Cape Town LK - https://open.uct.ac.za PB - University of Cape Town PY - 1998 T1 - A study of integrability conditions for irrotational dust spacetimes TI - A study of integrability conditions for irrotational dust spacetimes UR - http://hdl.handle.net/11427/21328 ER - en_ZA
dc.identifier.urihttp://hdl.handle.net/11427/21328
dc.identifier.vancouvercitationLesame WM. A study of integrability conditions for irrotational dust spacetimes. [Thesis]. University of Cape Town ,Faculty of Science ,Department of Mathematics and Applied Mathematics, 1998 [cited yyyy month dd]. Available from: http://hdl.handle.net/11427/21328en_ZA
dc.language.isoengen_ZA
dc.publisher.departmentDepartment of Mathematics and Applied Mathematicsen_ZA
dc.publisher.facultyFaculty of Scienceen_ZA
dc.publisher.institutionUniversity of Cape Town
dc.subject.otherMathematics and Applied Mathematicsen_ZA
dc.titleA study of integrability conditions for irrotational dust spacetimesen_ZA
dc.typeDoctoral Thesis
dc.type.qualificationlevelDoctoral
dc.type.qualificationnamePhDen_ZA
uct.type.filetypeText
uct.type.filetypeImage
uct.type.publicationResearchen_ZA
uct.type.resourceThesisen_ZA
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