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arXiv · 1706.08426

The Hawking-Penrose singularity theorem for $C^{1,1}$-Lorentzian metrics

Melanie Graf·James D. E. Grant·Michael Kunzinger·Roland Steinbauer
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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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Melanie Graf, James D. E. Grant, Michael Kunzinger, Roland Steinbauer. 2017-06-26. The Hawking-Penrose singularity theorem for $C^{1,1}$-Lorentzian metrics. https://doi.org/10.1007/s00220-017-3047-y

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