English

A note on the Lorentzian splitting theorem

Differential Geometry 2025-04-22 v2 General Relativity and Quantum Cosmology

Abstract

We present a version of the Lorentzian splitting theorem under a weakened Ricci curvature condition. The proof makes use of basic properties of achronal limits [19], [20], together with the geometric maximum principle for C0C^0 spacelike hypersurfaces in [1]. Our version strengthens a related result in [29] in the globally hyperbolic setting by removing a certain boundedness condition on the Ricci curvature.

Keywords

Cite

@article{arxiv.2504.05028,
  title  = {A note on the Lorentzian splitting theorem},
  author = {Gregory J. Galloway},
  journal= {arXiv preprint arXiv:2504.05028},
  year   = {2025}
}

Comments

12 pages; v2: a pertinent reference, and some related comments, added. Title and abstract also modified

R2 v1 2026-06-28T22:49:21.877Z