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Communications in Mathematical Physics

, Volume 360, Issue 3, pp 1009–1042 | Cite as

The Hawking–Penrose Singularity Theorem for C 1,1-Lorentzian Metrics

  • Melanie Graf
  • James D. E. Grant
  • Michael Kunzinger
  • Roland Steinbauer
Article

Abstract

We show that the Hawking–Penrose singularity theorem, and the generalisation of this theorem due to Galloway and Senovilla, continue to hold for Lorentzian metrics that are of C 1,1-regularity. We formulate appropriate weak versions of the strong energy condition and genericity condition for C 1,1-metrics, and of C 0-trapped submanifolds. By regularisation, we show that, under these weak conditions, causal geodesics necessarily become non-maximising. This requires a detailed analysis of the matrix Riccati equation for the approximating metrics, which may be of independent interest.

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Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2017

Authors and Affiliations

  1. 1.Faculty of MathematicsUniversity of ViennaViennaAustria
  2. 2.Department of MathematicsUniversity of SurreyGuildfordUK

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