A study of integrability conditions for irrotational dust spacetimes

 

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dc.contributor.advisor Ellis, George F R en_ZA
dc.contributor.author Lesame, William Mphepeng en_ZA
dc.date.accessioned 2016-08-18T13:51:02Z
dc.date.available 2016-08-18T13:51:02Z
dc.date.issued 1998 en_ZA
dc.identifier.citation Lesame, W. 1998. A study of integrability conditions for irrotational dust spacetimes. University of Cape Town. en_ZA
dc.identifier.uri http://hdl.handle.net/11427/21328
dc.description Bibliography: pages 139-145. en_ZA
dc.description.abstract 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. en_ZA
dc.language.iso eng en_ZA
dc.subject.other Mathematics and Applied Mathematics en_ZA
dc.title A study of integrability conditions for irrotational dust spacetimes en_ZA
dc.type Thesis / Dissertation en_ZA
uct.type.publication Research en_ZA
uct.type.resource Thesis en_ZA
dc.publisher.institution University of Cape Town
dc.publisher.faculty Faculty of Science en_ZA
dc.publisher.department Department of Mathematics and Applied Mathematics en_ZA
dc.type.qualificationlevel Doctoral en_ZA
dc.type.qualificationname PhD en_ZA
uct.type.filetype Text
uct.type.filetype Image


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