Manifold joins and jump conditions in general relativity

 

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dc.contributor.advisor Ellis, George F R en_ZA
dc.contributor.author Baston, Robert James en_ZA
dc.date.accessioned 2016-10-21T07:32:47Z
dc.date.available 2016-10-21T07:32:47Z
dc.date.issued 1982 en_ZA
dc.identifier.citation Baston, R. 1982. Manifold joins and jump conditions in general relativity. University of Cape Town. en_ZA
dc.identifier.uri http://hdl.handle.net/11427/22232
dc.description.abstract 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. en_ZA
dc.language.iso eng en_ZA
dc.subject.other Applied Mathematics en_ZA
dc.title Manifold joins and jump conditions in general relativity en_ZA
dc.type Master Thesis
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 Masters
dc.type.qualificationname MSc en_ZA
uct.type.filetype Text
uct.type.filetype Image
dc.identifier.apacitation Baston, 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/11427/22232 en_ZA
dc.identifier.chicagocitation Baston, 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/11427/22232 en_ZA
dc.identifier.vancouvercitation Baston 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/11427/22232 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


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