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- Title
Timelike Ricci bounds for low regularity spacetimes by optimal transport.
- Authors
Braun, Mathias; Calisti, Matteo
- 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.
- Subjects
RENYI'S entropy; GEODESICS; SPACETIME; SENSES; EQUATIONS
- Publication
Communications in Contemporary Mathematics, 2024, Vol 26, Issue 9, p1
- ISSN
0219-1997
- Publication type
Article
- DOI
10.1142/S0219199723500499