Hawking's singularity theorem for Lipschitz Lorentzian metrics
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arXiv
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| Main Authors: | , , , , |
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866911315849641984 |
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| author | Calisti, Matteo Graf, Melanie Hafemann, Eduardo Kunzinger, Michael Steinbauer, Roland |
| author_facet | Calisti, Matteo Graf, Melanie Hafemann, Eduardo Kunzinger, Michael Steinbauer, Roland |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2501_18450 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Hawking's singularity theorem for Lipschitz Lorentzian metrics Calisti, Matteo Graf, Melanie Hafemann, Eduardo Kunzinger, Michael Steinbauer, Roland Differential Geometry General Relativity and Quantum Cosmology Mathematical Physics 83C75, 53C50, 46T30 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. |
| title | Hawking's singularity theorem for Lipschitz Lorentzian metrics |
| topic | Differential Geometry General Relativity and Quantum Cosmology Mathematical Physics 83C75, 53C50, 46T30 |
| url | https://arxiv.org/abs/2501.18450 |