Manifold joins and jump conditions in general relativity

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dc.contributor.advisorEllis, George F Ren_ZA
dc.contributor.authorBaston, Robert Jamesen_ZA
dc.date.accessioned2016-10-21T07:32:47Z
dc.date.available2016-10-21T07:32:47Z
dc.date.issued1982en_ZA
dc.description.abstractThis thesis has as its aim the analysis of a possible manifold structure on V, a join of two individual manifolds V⁺ and V⁻, and analysing the physics across the join, as implied by Einstein's theory of General Relativity. There are several reasons why one might want to study such a situation. Firstly, the joining of manifolds is useful in the study of shock waves, be they of gravitational or other origin - we will be able to characterise the propagation of energy in the join. Secondly piecing together manifolds is a potentially fruitful way of obtaining exact solutions of Einstein's equations which do not exhibit any symmetries in the large, and are yet sufficiently homogeneous (in some sense) to enable one to model the apparent Universe - the prototype of this is the Swiss-Cheese model, used to study light transmission in an inhomogeneous Universe. Thirdly, discontinuities in the fundamental quantities in Relativity are of prime importance in the study of singularities and in particular, it is of prime importance to single out the contributions of the differential geometry and metric structure of the Universe to the existence and nature of such singularities. Closely linked to these problems is the problem of linking the small scale structure of the Universe (which is manifestly complicated and potentially full of singularities) and the large scale structure, which seems so well modelled by assumptions of homogeneity and isotropy. In this regard, the techniques of Regge (1961), originally proposed to provide approximate solutions to the Einstein equations, assume a new theoretical importance, for the delta-type singularities in the curvature he used, in a smoothing process, to represent the (assumed) continuous curvature of space, could in themselves play a distinguished role representing the small scale structure of the Universe. Furthermore, the matching together of blocks of space-time with sharp edges and corners may enable to develop a manifold like structure in which the tangent spaces of some points had a surfeit or deficiency of vectors, so that the differential geometry of the resulting space-time forced discontinuities and singularities in the metric structure of the Universe. Although this may be aphysical, it may be a reasonable way of seeking further understanding of the Universe.en_ZA
dc.identifier.apacitationBaston, R. J. (1982). <i>Manifold joins and jump conditions in general relativity</i>. (Thesis). University of Cape Town ,Faculty of Science ,Department of Mathematics and Applied Mathematics. Retrieved from http://hdl.handle.net/11427/22232en_ZA
dc.identifier.chicagocitationBaston, Robert James. <i>"Manifold joins and jump conditions in general relativity."</i> Thesis., University of Cape Town ,Faculty of Science ,Department of Mathematics and Applied Mathematics, 1982. http://hdl.handle.net/11427/22232en_ZA
dc.identifier.citationBaston, R. 1982. Manifold joins and jump conditions in general relativity. University of Cape Town.en_ZA
dc.identifier.ris TY - Thesis / Dissertation AU - Baston, Robert James AB - This thesis has as its aim the analysis of a possible manifold structure on V, a join of two individual manifolds V⁺ and V⁻, and analysing the physics across the join, as implied by Einstein's theory of General Relativity. There are several reasons why one might want to study such a situation. Firstly, the joining of manifolds is useful in the study of shock waves, be they of gravitational or other origin - we will be able to characterise the propagation of energy in the join. Secondly piecing together manifolds is a potentially fruitful way of obtaining exact solutions of Einstein's equations which do not exhibit any symmetries in the large, and are yet sufficiently homogeneous (in some sense) to enable one to model the apparent Universe - the prototype of this is the Swiss-Cheese model, used to study light transmission in an inhomogeneous Universe. Thirdly, discontinuities in the fundamental quantities in Relativity are of prime importance in the study of singularities and in particular, it is of prime importance to single out the contributions of the differential geometry and metric structure of the Universe to the existence and nature of such singularities. Closely linked to these problems is the problem of linking the small scale structure of the Universe (which is manifestly complicated and potentially full of singularities) and the large scale structure, which seems so well modelled by assumptions of homogeneity and isotropy. In this regard, the techniques of Regge (1961), originally proposed to provide approximate solutions to the Einstein equations, assume a new theoretical importance, for the delta-type singularities in the curvature he used, in a smoothing process, to represent the (assumed) continuous curvature of space, could in themselves play a distinguished role representing the small scale structure of the Universe. Furthermore, the matching together of blocks of space-time with sharp edges and corners may enable to develop a manifold like structure in which the tangent spaces of some points had a surfeit or deficiency of vectors, so that the differential geometry of the resulting space-time forced discontinuities and singularities in the metric structure of the Universe. Although this may be aphysical, it may be a reasonable way of seeking further understanding of the Universe. DA - 1982 DB - OpenUCT DP - University of Cape Town LK - https://open.uct.ac.za PB - University of Cape Town PY - 1982 T1 - Manifold joins and jump conditions in general relativity TI - Manifold joins and jump conditions in general relativity UR - http://hdl.handle.net/11427/22232 ER - en_ZA
dc.identifier.urihttp://hdl.handle.net/11427/22232
dc.identifier.vancouvercitationBaston RJ. Manifold joins and jump conditions in general relativity. [Thesis]. University of Cape Town ,Faculty of Science ,Department of Mathematics and Applied Mathematics, 1982 [cited yyyy month dd]. Available from: http://hdl.handle.net/11427/22232en_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.otherApplied Mathematicsen_ZA
dc.titleManifold joins and jump conditions in general relativityen_ZA
dc.typeMaster Thesis
dc.type.qualificationlevelMasters
dc.type.qualificationnameMScen_ZA
uct.type.filetypeText
uct.type.filetypeImage
uct.type.publicationResearchen_ZA
uct.type.resourceThesisen_ZA
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