Singularity theorems and the Lorentzian splitting theorem for the Bakry-Emery-Ricci tensor

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Abstract

We consider the Hawking-Penrose singularity theorems and the Lorentzian splitting theorem under the weaker curvature condition of nonnegative Bakry-Emery-Ricci curvature Ricfm in timelike directions. We prove that they still hold when m is finite, and when m is infinite, they hold under the additional assumption that f is bounded from above.

Original languageEnglish (US)
Pages (from-to)477-490
Number of pages14
JournalJournal of Geometry and Physics
Volume60
Issue number3
DOIs
StatePublished - Mar 2010

All Science Journal Classification (ASJC) codes

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

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