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Filtering by: Academic Affiliation Mathematics Remove constraint Academic Affiliation: Mathematics Creator Hellaby, Charles Remove constraint Creator: Hellaby, Charles Peer Reviewed Yes Remove constraint Peer Reviewed: Yes Resource Type Article Remove constraint Resource Type: Article Rights Statement Copyright Not Evaluated Remove constraint Rights Statement: Copyright Not Evaluated

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  • The patchwork divergence theorem

    Creator:
    Dray, Tevian and Hellaby, Charles
    Abstract:
    The divergence theorem in its usual form applies only to suitably smooth vector fields. For vector fields which are merely piecewise smooth, as is natural at a boundary between regions with different physical properties, one must patch together the divergence theorem applied separately in each region. We give an elegant...
    Resource Type:
    Article

  • Failure of standard conservation laws at a classical change of signature

    Creator:
    Hellaby, Charles and Dray, Tevian
    Abstract:
    The divergence theorem as usually stated cannot be applied across a change of signature unless it is reexpressed to allow for a finite source term on the signature change surface. Consequently all conservation laws must also be ‘‘modified,’’ and therefore insistence on conservation of matter across such a surface cannot...
    Resource Type:
    Article

  • Reply Comment: Comparison of approaches to classical signature change

    Creator:
    Hellaby, Charles and Dray, Tevian
    Abstract:
    We contrast the two approaches to ‘‘classical’’ signature change used by Hayward with the one used by us (Hellaby and Dray). There is (as yet) no rigorous derivation of appropriate distributional field equations. Hayward’s distributional approach is based on a postulated modified form of the field equations. We make an...
    Resource Type:
    Article