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<p>We prove Hawking’s singularity theorem for spacetime metrics of local Lipschitz regularity. The proof rests on (1) new estimates for the Ricci curvature of regularising smooth metrics that are based upon a quite general Friedrichs-type lemma and (2) the replacement of the usual focusing techniques for timelike geodesics—which in the absence of a classical ODE-theory for the initial value problem are no longer available—by a worldvolume estimate based on a segment-type inequality that allows one to control the volume of the set of points in a spacelike surface that possess long maximisers.</p>

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Hawking’s Singularity Theorem for Lipschitz Lorentzian Metrics

  • 期刊论文

  • 出版模式：

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  • 发表日期：

    2025年8月1日

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  • Matteo Calisti,
  • Melanie Graf,
  • Eduardo Hafemann,
  • Michael Kunzinger,
  • Roland Steinbauer

摘要

We prove Hawking’s singularity theorem for spacetime metrics of local Lipschitz regularity. The proof rests on (1) new estimates for the Ricci curvature of regularising smooth metrics that are based upon a quite general Friedrichs-type lemma and (2) the replacement of the usual focusing techniques for timelike geodesics—which in the absence of a classical ODE-theory for the initial value problem are no longer available—by a worldvolume estimate based on a segment-type inequality that allows one to control the volume of the set of points in a spacelike surface that possess long maximisers.