Hawking's singularity theorem for $C^{1,1}$-metrics

Abstract

We provide a detailed proof of Hawking's singularity theorem in the regularity class $C^{1,1}$, i.e., for spacetime metrics possessing locally Lipschitz continuous first derivatives. The proof uses recent results in $C^{1,1}$-causality theory and is based on regularisation techniques adapted to the causal structure.

19 pages, LaTeX; v2: corrected Lemma 4.2; v3: typos corrected, final version

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• Singularity Theorems and Their Consequences
• The 1965 Penrose singularity theorem
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• Holographic applications of logarithmic conformal field theories
• Limit curve theorems in Lorentzian geometry
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