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Abstract
We prove that a globally hyperbolic smooth spacetime endowed with a C1-Lorentzian metric whose Ricci tensor is bounded from below in all timelike directions, in a distributional sense, obeys the timelike measure-contraction property. This result includes a class of spacetimes with borderline regularity for which local existence results for the vacuum Einstein equation are known in the setting of spaces with timelike Ricci bounds in a synthetic sense. In particular, these spacetimes satisfy timelike Brunn-Minkowski, Bonnet-Myers, and Bishop-Gromov inequalities in sharp form, without any timelike nonbranching assumption. If the metric is even C1,1, in fact the stronger timelike curvature-dimension condition holds. In this regularity, we also obtain uniqueness of chronological optimal couplings and chronological geodesics.
Originalsprache | Englisch |
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Aufsatznummer | 2350049 |
Seitenumfang | 30 |
Fachzeitschrift | Communications in Contemporary Mathematics |
Jahrgang | 26 |
Ausgabenummer | 9 |
DOIs | |
Publikationsstatus | Veröffentlicht - 1 Nov. 2024 |
ÖFOS 2012
- 101002 Analysis
- 101006 Differentialgeometrie
- 103028 Relativitätstheorie
- 101009 Geometrie
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Thematic Program on Nonsmooth Riemannian and Lorentzian Geometry - Workshop on Mathematical Relativity, Scalar Curvature and Synthetic Lorentzian Geometry
Matteo Calisti (Vortragende*r)
3 Okt. 2022 → 14 Okt. 2022Aktivität: Vorträge › Vortrag › Science to Science