The Penrose singularity theorem in regularity $C^{1,1}$

TL;DR

This paper extends the Penrose singularity theorem to spacetimes with metrics of regularity C^{1,1}, using regularisation techniques and recent low regularity causality theory results.

Contribution

It introduces a new proof of the Penrose theorem applicable to C^{1,1} regularity metrics, broadening its applicability.

Findings

Validates Penrose theorem for C^{1,1} metrics

Uses regularisation techniques in low regularity causality

Connects recent causality theory results with singularity theorems

Abstract

We extend the validity of the Penrose singularity theorem to spacetime metrics of regularity $C^{1,1}$. The proof is based on regularisation techniques, combined with recent results in low regularity causality theory.