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 KunzingerEmail author
  • Roland Steinbauer


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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© 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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