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

Understand

We extend both the Hawking-Penrose Theorem and its generalisation due to Galloway and Senovilla to Lorentzian metrics of regularity $C^1$.

• For metrics of such low regularity, two main obstacles have to be addressed.
• On the one hand, the Ricci tensor now is distributional, and on the other hand, unique solvability of the geodesic equation is lost.
• To deal with the first issue in a consistent way, we develop a theory of tensor distributions of finite order, which also provides a framework for the recent proofs of the theorems of Hawking and of Penrose for $C^1$-metrics [7].