The Hawking–Penrose Singularity Theorem for C1,1-Lorentzian Metrics

@article{Graf2017TheHS,
  title={The Hawking–Penrose Singularity Theorem for C1,1-Lorentzian Metrics},
  author={Melanie Graf and James D E Grant and Michael Kunzinger and Roland Steinbauer},
  journal={Communications in Mathematical Physics},
  year={2017},
  volume={360},
  pages={1009-1042}
}
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 C1,1-regularity. We formulate appropriate weak versions of the strong energy condition and genericity condition for C1,1-metrics, and of C0-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… 
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