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  • 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...
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    approaches to classical signature change Charles Hellaby* Department of Applied Mathematics, University of

  • 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...
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    thank the FRD for a research grant. ’ Charles Hellaby and Tevian Dray, “Failure of Standard

  • 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...
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    conservation laws at a classical change of signature Charles Hellaby' Department of App/ied Mathematics

  • Einstein’s equations in the presence of signature change

    Creator:
    Dray, Tevian
    Abstract:
    We discuss Einstein’s field equations in the presence of signature change using variational methods, obtaining a generalization of the Lanczos equation relating the distributional term in the stress tensor to the discontinuity of the extrinsic curvature. In particular, there is no distributional term in the stress tensor, and hence no...
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    , John Friedman, David Hartley, Charles Hellaby, Marcus Kriele, Malcolm MacCallum, Corinne Manogue, Jo¨rg

  • Scalar field equation in the presence of signature change

    Creator:
    Dray, Tevian, Manogue, Corinne A., and Tucker, Robin W.
    Abstract:
    We consider the (massless) scalar field on a two-dimensional manifold with metric that changes signature from Lorentzian to Euclidean. Requiring a conserved momentum in the spatially homogeneous case leads to a particular choice of propagation rule. The resulting mix of positive and negative frequencies depends only on the total (conformal)...
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    Hayward, Charles Hellaby, Joe Ro- mano, Abe Taub, and Phillip Tuckey for helpful con- versations. R.W.T