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.
A note on the Lorentzian splitting theorem
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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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A Lorentzian splitting theorem for continuously differentiable metrics and weights
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.