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arXiv · 2507.06836

A Lorentzian splitting theorem for continuously differentiable metrics and weights

Mathias Braun·Nicola Gigli·Robert J. McCann·Argam Ohanyan·Clemens Sämann
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Abstract

We prove a splitting theorem for globally hyperbolic, weighted spacetimes with metrics and weights of regularity $C^1$ by combining elliptic techniques for the negative homogeneity $p$-d'Alembert operator from our recent work in the smooth setting with the concept of line-adapted curves introduced here. Our results extend the Lorentzian splitting theorem proved for smooth globally hyperbolic spacetimes by Galloway -- and variants of its weighted counterparts by Case and Woolgar--Wylie -- to this low regularity setting.

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Mathias Braun, Nicola Gigli, Robert J. McCann, Argam Ohanyan, Clemens Sämann. 2025-07-09. A Lorentzian splitting theorem for continuously differentiable metrics and weights. https://arxiv.org/abs/2507.06836

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