Titel
The Hawking–Penrose Singularity Theorem for C1-Lorentzian Metrics
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Abstract
We extend both the Hawking–Penrose theorem and its generalisation due to Galloway and Senovilla to Lorentzian metrics of regularity C1. 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 C1-metrics (Graf in Commun Math Phys 378(2):1417–1450, 2020). For the second issue, we study geodesic branching and add a further alternative to causal geodesic incompleteness to the theorem, namely a condition of maximal causal non-branching. The genericity condition is re-cast in a distributional form that applies to the current reduced regularity while still being fully compatible with the smooth and C1,1-settings. In addition, we develop refinements of the comparison techniques used in the proof of the C1,1-version of the theorem (Graf in Commun Math Phys 360:1009–1042, 2018). The necessary results from low regularity causality theory are collected in an appendix.
Stichwort
Mathematical PhysicsStatistical and Nonlinear Physics
Objekt-Typ
Sprache
Englisch [eng]
Persistent identifier
Erschienen in
Titel
Communications in Mathematical Physics
Band
391
Ausgabe
3
ISSN
0010-3616
Erscheinungsdatum
2022
Seitenanfang
1143
Seitenende
1179
Publication
Springer Science and Business Media LLC
Erscheinungsdatum
2022
Zugänglichkeit
Rechte
Rechteangabe
© The Author(s) 2022
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