We prove that a globally hyperbolic smooth spacetime endowed with a C 1 -Lorentzian metric whose Ricci tensor is bounded from below in all timelike directions, in a distributional sense, obeys the timelike measurecontraction 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 C 1,1 , in fact the stronger timelike curvature-dimension condition holds. In this regularity, we also obtain uniqueness of chronological optimal couplings and chronological geodesics. Contents 1. Introduction 2. Spacetimes of low regularity 2.1. Terminology 2.2. C 1 -spacetimes as Lorentzian geodesic spaces 2.3. Approximation 2.4. Lorentzian optimal transport 3. Proofs of the main results 3.1
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