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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Communicated by P. T. Chrusciel
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Graf, M., Grant, J.D.E., Kunzinger, M. et al. The Hawking–Penrose Singularity Theorem for C 1,1-Lorentzian Metrics. Commun. Math. Phys. 360, 1009–1042 (2018). https://doi.org/10.1007/s00220-017-3047-y
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DOI: https://doi.org/10.1007/s00220-017-3047-y