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

TL;DR

This paper offers a detailed proof of Hawking's singularity theorem for spacetimes with $C^{1,1}$ metrics, expanding the theorem's applicability to less smooth geometries using advanced causality and regularisation methods.

Contribution

It provides the first comprehensive proof of Hawking's singularity theorem for $C^{1,1}$-metrics, utilizing recent causality theory and regularisation techniques.

Findings

Proof extends Hawking's theorem to $C^{1,1}$-metrics

Uses new causality results in $C^{1,1}$-spacetimes

Employs regularisation methods for causal structure

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.