Curvature-dimension bounds for Lorentzian splitting theorems

Eric Woolgar, William Wylie

Research output: Contribution to journalArticle

Abstract

We analyze Lorentzian spacetimes subject to curvature-dimension bounds using the Bakry–Émery–Ricci tensor. We extend the Hawking–Penrose type singularity theorem and the Lorentzian timelike splitting theorem to synthetic dimensions N≤1, including all negative synthetic dimensions. The rigidity of the timelike splitting reduces to a warped product splitting when N=1. We also extend the null splitting theorem of Lorentzian geometry, showing that it holds under a null curvature-dimension bound on the Bakry–Émery–Ricci tensor for all N∈(−∞,2]∪(n,∞) and for the N=∞ case as well, with reduced rigidity if N=2. In consequence, the basic singularity and splitting theorems of Lorentzian Bakry-Émery theory now cover all synthetic dimensions for which such theorems are possible. The splitting theorems are found always to exhibit reduced rigidity at the critical synthetic dimension.

Original languageEnglish (US)
Pages (from-to)131-145
Number of pages15
JournalJournal of Geometry and Physics
Volume132
DOIs
StatePublished - Oct 2018

Keywords

  • Bakry–Emery–Ricci curvature
  • Lorentzian geometry
  • Singularity theorems
  • Splitting theorems

ASJC Scopus subject areas

  • Mathematical Physics
  • Physics and Astronomy(all)
  • Geometry and Topology

Fingerprint Dive into the research topics of 'Curvature-dimension bounds for Lorentzian splitting theorems'. Together they form a unique fingerprint.

  • Cite this