BRADFORD SCHOLARS

    • Sign in
    View Item 
    •   Bradford Scholars
    • University of Bradford eTheses
    • Theses
    • View Item
    •   Bradford Scholars
    • University of Bradford eTheses
    • Theses
    • View Item
    JavaScript is disabled for your browser. Some features of this site may not work without it.

    Browse

    All of Bradford ScholarsCommunitiesAuthorsTitlesSubjectsPublication DateThis CollectionAuthorsTitlesSubjectsPublication Date

    My Account

    Sign in

    HELP

    Bradford Scholars FAQsCopyright Fact SheetPolicies Fact SheetDeposit Terms and ConditionsDigital Preservation Policy

    Statistics

    Most Popular ItemsStatistics by CountryMost Popular Authors

    Conformal symmetries in special and general relativity.The derivation and interpretation of conformal symmetries and asymptotic conformal symmetries in Minkowski space-time and in some space-times of general relativity.

    • CSV
    • RefMan
    • EndNote
    • BibTex
    • RefWorks
    Thumbnail
    View/Open
    Griffin.pdf (6.446Mb)
    Download
    Publication date
    2009-10-28T16:29:40Z
    Author
    Griffin, G.K.
    Supervisor
    Robinson, W.J.
    Keyword
    Asymptotic conformal Killing vectors
    Asymptotically-flat space-times
    General relativity
    Minkowski space-time
    Rights
    Creative Commons License
    The University of Bradford theses are licenced under a Creative Commons Licence.
    Institution
    University of Bradford
    Department
    Postgraduate School of Studies in Mathematics.
    Awarded
    1976
    
    Metadata
    Show full item record
    Abstract
    The central objective of this work is to present an analysis of the asymptotic conformal Killing vectors in asymptotically-flat space-times of general relativity. This problem has been examined by two different methods; in Chapter 5 the asymptotic expansion technique originated by Newman and Unti [31] leads to a solution for asymptotically-flat spacetimes which admit an asymptotically shear-free congruence of null geodesics, and in Chapter 6 the conformal rescaling technique of Penrose [54] is used both to support the findings of the previous chapter and to set out a procedure for solution in the general case. It is pointed out that Penrose's conformal technique is preferable to the use of asymptotic expansion methods, since it can be established in a rigorous manner without leading to the possible convergence difficulties associated with asymptotic expansions. Since the asymptotic conformal symmetry groups of asymptotically flat space-times Are generalisations of the conformal group of Minkowski space-time we devote Chapters 3 and 4 to a study of the flat space case so that the results of later chapters may receive an interpretation in terms of familiar concepts. These chapters fulfil a second, equally important, role in establishing local isomorphisms between the Minkowski-space conformal group, 90(2,4) and SU(2,2). The SO(2,4) representation has been used by Kastrup [61] to give a physical interpretation using space-time gauge transformations. This appears as part of the survey of interpretative work in Chapter 7. The SU(2,2) representation of the conformal group has assumed a theoretical prominence in recent years. through the work of Penrose [9-11] on twistors. In Chapter 4 we establish contact with twistor ideas by showing that points in Minkowski space-time correspond to certain complex skew-symmetric rank two tensors on the SU(2,2) carrier space. These objects are, in Penrose's terminology [91, simple skew-symmetric twistors of valence [J. A particularly interesting aspect of conformal objects in space-time is explored in Chapter 8, where we extend the work of Geroch [16] on multipole moments of the Laplace equation in 3-space to the consideration. of Q tý =0 in Minkowski space-time. This development hinges upon the fact that multipole moment fields are also conformal Killing tensors. In the final chapter some elementary applications of the results of Chapters 3 and 5 are made to cosmological models which have conformal flatness or asymptotic conformal flatness. In the first class here we have 'models of the Robertson-Walker type and in the second class we have the asymptotically-Friedmann universes considered by Hawking [73].
    URI
    http://hdl.handle.net/10454/3796
    Type
    Thesis
    Qualification name
    PhD
    Collections
    Theses

    entitlement

     
    DSpace software (copyright © 2002 - 2023)  DuraSpace
    Quick Guide | Contact Us
    Open Repository is a service operated by 
    Atmire NV
     

    Export search results

    The export option will allow you to export the current search results of the entered query to a file. Different formats are available for download. To export the items, click on the button corresponding with the preferred download format.

    By default, clicking on the export buttons will result in a download of the allowed maximum amount of items.

    To select a subset of the search results, click "Selective Export" button and make a selection of the items you want to export. The amount of items that can be exported at once is similarly restricted as the full export.

    After making a selection, click one of the export format buttons. The amount of items that will be exported is indicated in the bubble next to export format.