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A note on the Lorentzian splitting theorem

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arxiv 2504.05028 v2 pith:45LXPYZI submitted 2025-04-07 math.DG gr-qc

Gregory J. Galloway This is my paper · ORCID
classification math.DGgr-qc
keywords conditioncurvaturelorentzianriccisplittingtheoremversionachronal
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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 $C^0$ 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.

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  1. A Lorentzian splitting theorem for continuously differentiable metrics and weights

    math.DG 2025-07 accept novelty 7.0 of 10

    A Lorentzian splitting theorem holds for C^1 metrics and weights: a complete timelike line forces the spacetime to split as R times a Riemannian factor.

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