PreprintCC BY 4.0arXiv
The Hawking and Penrose singularity theorems for low regularity Finsler spacetimes
Abstract
We prove the Hawking and Penrose singularity theorems for Lorentz--Finsler structures of mixed horizontal/vertical regularity C(1,2) in the C1 weighted case and C(1,3) in the unweighted case. At this regularity, geodesics need not be uniquely determined by their initial conditions, and the (weighted) Ricci curvature must be interpreted distributionally. Our approach relies on a two-stage approximation procedure: first, a homogeneity-preserving convolution, which is of independent interest in the broader semi-Riemann--Finsler setting, and second, a causality-adapted approximation à la Chruściel--Grant. In the special case of C1 Lorentzian metrics, our results extend the C1 singularity theorems of Graf to the C1 weighted case.
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BibTeX
@misc{eros2026hawking,
title = {{The Hawking and Penrose singularity theorems for low regularity Finsler spacetimes}},
author = {Darius Erös and Ettore Minguzzi and Argam Ohanyan and Shin-ichi Ohta},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.11911},
eprint = {2610.11911},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.11911},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - The Hawking and Penrose singularity theorems for low regularity Finsler spacetimes
AU - Darius Erös
AU - Ettore Minguzzi
AU - Argam Ohanyan
AU - Shin-ichi Ohta
PY - 2026
DA - 2026/10/08
PB - arXiv
DO - 10.48550/arxiv.2610.11911
UR - https://arxiv.org/abs/2610.11911
AB - We prove the Hawking and Penrose singularity theorems for Lorentz--Finsler structures of mixed horizontal/vertical regularity C^(1,2) in the C^1 weighted case and C^(1,3) in the unweighted case. At this regularity, geodesics need not be uniquely determined by their initial conditions, and the (weighted) Ricci curvature must be interpreted distributionally. Our approach relies on a two-stage approximation procedure: first, a homogeneity-preserving convolution, which is of independent interest in the broader semi-Riemann--Finsler setting, and second, a causality-adapted approximation à la Chruściel--Grant. In the special case of C^1 Lorentzian metrics, our results extend the C^1 singularity theorems of Graf to the C^1 weighted case.
ER -