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A regularisation approach to causality theory for \(C^{1,1}\)-Lorentzian metrics

  • Michael Kunzinger
  • Roland Steinbauer
  • Milena Stojković
  • James A.  Vickers
Research Article

Abstract

We show that many standard results of Lorentzian causality theory remain valid if the regularity of the metric is reduced to \(C^{1,1}\). Our approach is based on regularisations of the metric adapted to the causal structure.

Keywords

Causality theory Low regularity Regularisation Exponential map 

Notes

Acknowledgments

We would like to thank James D. E. Grant for helpful discussions. The authors acknowledge the support of FWF projects P23714 and P25326, as well as OeAD project WTZ CZ 15/2013. We are indebted to the referees of this paper for several comments that have led to substantial improvements in the presentation.

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Copyright information

© Springer Science+Business Media New York 2014

Authors and Affiliations

  • Michael Kunzinger
    • 1
  • Roland Steinbauer
    • 1
  • Milena Stojković
    • 1
  • James A.  Vickers
    • 2
  1. 1.Faculty of MathematicsUniversity of ViennaViennaAustria
  2. 2.School of Mathematical SciencesUniversity of SouthamptonSouthamptonUK

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