Timelike Ricci bounds for low regularity spacetimes by optimal transport

Mathias Braun (Korresp. Autor*in), Matteo Calisti

Veröffentlichungen: Beitrag in FachzeitschriftArtikelPeer Reviewed

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.

OriginalspracheEnglisch
Aufsatznummer2350049
Seitenumfang30
FachzeitschriftCommunications in Contemporary Mathematics
Jahrgang26
Ausgabenummer9
DOIs
PublikationsstatusVeröffentlicht - 1 Nov. 2024

ÖFOS 2012

  • 101002 Analysis
  • 101006 Differentialgeometrie
  • 103028 Relativitätstheorie
  • 101009 Geometrie

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