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arXiv · 2609.05167

Spherically symmetric inextendibility of weak null singularities with Christoffel symbols in $L^s_{\text{loc}}$

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 $L^{s}_{\text{loc}}$ 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-Nordstr\"{o}m-Vaidya spacetime as well as by a class of spacetimes arising from small and generic spherically symmetric perturbations of subextremal Reissner-Nordstr\"{o}m under the Einstein-Maxwell-scalar field system.

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Peter Cameron, Jan Sbierski. 2026-09-04. Spherically symmetric inextendibility of weak null singularities with Christoffel symbols in $L^s_{\text{loc}}$. https://arxiv.org/abs/2609.05167

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