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Comment on “smooth and discontinuous signature change in general relativity”

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Abstract

Kossowski and Kriele derived boundary conditions on the metric at a surface of signature change. We point out that their derivation is based not only on certain smoothness assumptions but also on a postulated form of the Einstein field equations. Since there is no canonical form of the field equations at a change of signature, their conclusions are not inescapable. We show here that a weaker formulation is possible, in which less restrictive smoothness assumptions are made, and (a slightly different form of) the Einstein field equations are satisfied. In particular, in this formulation it is possible to have a bounded energy-momentum tensor at a change of signature without satisfying their condition that the extrinsic curvature vanish.

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Author notes

  1. Tevian Dray

    Present address: Department of Mathematics, Oregon State University, 97331, Corvallis, Oregon, USA

Authors and Affiliations

  1. School of Physics & Chemistry, Lancaster University, LA1 4YB, Lancaster, UK

    Tevian Dray

  2. Department of Applied Mathematics, University of Cape Town, 7700, Rondebosch, South Africa

    Charles Hellaby

Authors
  1. Tevian Dray
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  2. Charles Hellaby
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Dray, T., Hellaby, C. Comment on “smooth and discontinuous signature change in general relativity”. Gen Relat Gravit 28, 1401–1407 (1996). https://doi.org/10.1007/BF02109530

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  • DOI: https://doi.org/10.1007/BF02109530

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