• Login
    View Item 
    •   Home
    • Graduate Theses, Dissertations and Projects
    • Queen's Graduate Theses and Dissertations
    • View Item
    •   Home
    • Graduate Theses, Dissertations and Projects
    • Queen's Graduate Theses and Dissertations
    • View Item
    JavaScript is disabled for your browser. Some features of this site may not work without it.

    Defining gravitational singularities in general relativity

    Thumbnail
    View/Open
    Wurster_James_H_200807_MSc.pdf (4.444Mb)
    Date
    2008-07-22
    Author
    Wurster, James Howard
    Metadata
    Show full item record
    Abstract
    Singularities have been a long-standing problem in general relativity. In all other fields of physics, singularities can be easily located and avoided; in general relativity, singularities have an impact on the creation of the manifold, but, by definition, are not even part of real spacetime. Moreover, all singularities in general relativity cannot be treated in the same manner; thus, the classification of singularities is essential in order to understand them. One important class of singularities is curvature singularities, which, in some cases, can be subclassified as central, shell focusing or shell crossing singularities. We propose to further classify curvature singularities as either gravitational or non-gravitational.

    In general relativity, a curvature singularity is ``located'' where the scalar invariants of the spacetime are undefined. The gradient field of a non-zero scalar invariant can then be calculated, and the end points of the associated integral curves can be determined. If integral curves are attracted to (i.e. intersect) the singularity, then it is a gravitational singularity; if the integral curves avoid the singularity, then it is a non-gravitational singularity.

    We will test our method by analysing several different spacetimes, including Friedman-Lemaitre-Robertson-Walker, Schwarzschild, self-similar Vaidya, self-similar Tolman-Bondi, non-self-similar Vaidya, and Kerr spacetimes. We find that in every case studied, the integral curves have specific end points, therefore they can be used to classify a curvature singularity as gravitational or non-gravitational.

    In Friedman-Lemaitre-Robertson-Walker and Schwarzschild spacetimes, we determined that the a(t) = 0 and r = 0 singularities, respectively, are gravitational singularities. In Vaidya and Tolman-Bondi spacetime, we determine that the massless shell focusing singularities are non-gravitational singularities and that the central singularities (which have mass) are gravitational singularities. We also find that the non-gravitational singularities are the only singularities that have the possibility of being naked.

    In summary, we can determine which singularities are gravitational and which are non-gravitational by our method of examining the end points of the integral curves, which are constructed from the gradient field of scalar invariants.
    URI for this record
    http://hdl.handle.net/1974/1332
    Collections
    • Queen's Graduate Theses and Dissertations
    • Department of Physics, Engineering Physics and Astronomy Graduate Theses
    Request an alternative format
    If you require this document in an alternate, accessible format, please contact the Queen's Adaptive Technology Centre

    DSpace software copyright © 2002-2015  DuraSpace
    Contact Us
    Theme by 
    Atmire NV
     

     

    Browse

    All of QSpaceCommunities & CollectionsPublished DatesAuthorsTitlesSubjectsTypesThis CollectionPublished DatesAuthorsTitlesSubjectsTypes

    My Account

    LoginRegister

    Statistics

    View Usage StatisticsView Google Analytics Statistics

    DSpace software copyright © 2002-2015  DuraSpace
    Contact Us
    Theme by 
    Atmire NV