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PreprintCC BY 4.0arXiv

Spherically symmetric inextendibility of weak null singularities with Christoffel symbols in Lsloc

  • Peter Cameron
  • Jan Sbierski
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Abstract

Motivated by the strong cosmic censorship conjecture in general relativity, we prove the inextendibility of spherically symmetric weak null singularities as spherically symmetric Lorentzian manifolds with a continuous metric and Christoffel symbols in Lsloc for s>1. The result assumes a suitable blow-up condition on the derivative of the area-radius function transverse to the weak null singularity in combination with a rigidity result on continuous spherically symmetric extensions across null boundaries proven in [1]. In particular we show that these assumptions are satisfied by the Reissner-Nordström-Vaidya spacetime as well as by a class of spacetimes arising from small and generic spherically symmetric perturbations of subextremal Reissner-Nordström under the Einstein-Maxwell-scalar field system.

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Cite

BibTeXRIS
BibTeX
@misc{cameron2026spherically,
  title = {{Spherically symmetric inextendibility of weak null singularities with Christoffel symbols in $L^s_\textloc$}},
  author = {Peter Cameron and Jan Sbierski},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2609.05167},
  eprint = {2609.05167},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2609.05167},
  note = {CC BY 4.0},
}
RIS
TY  - UNPB
TI  - Spherically symmetric inextendibility of weak null singularities with Christoffel symbols in L^s_loc
AU  - Peter Cameron
AU  - Jan Sbierski
PY  - 2026
DA  - 2026/09/04
PB  - arXiv
DO  - 10.48550/arxiv.2609.05167
UR  - https://arxiv.org/abs/2609.05167
AB  - Motivated by the strong cosmic censorship conjecture in general relativity, we prove the inextendibility of spherically symmetric weak null singularities as spherically symmetric Lorentzian manifolds with a continuous metric and Christoffel symbols in L^s_loc for s>1. The result assumes a suitable blow-up condition on the derivative of the area-radius function transverse to the weak null singularity in combination with a rigidity result on continuous spherically symmetric extensions across null boundaries proven in [1]. In particular we show that these assumptions are satisfied by the Reissner-Nordström-Vaidya spacetime as well as by a class of spacetimes arising from small and generic spherically symmetric perturbations of subextremal Reissner-Nordström under the Einstein-Maxwell-scalar field system.
ER  -