Lipschitz inextendibility of weak null singularities from curvature blow-up

Abstract

We prove the $C_{\mathrm{loc}}^{0,1}$-inextendibility of weak null singularities without any symmetry assumptions. The proof introduces a new strategy to infer $C_{\mathrm{loc}}^{0,1}$-inextendibility from the blow-up of curvature. The assumed blow-up is expected to be satisfied for weak null singularities in the interior of generic rotating black holes. Thus, we expect the result presented here to directly contribute to the resolution of the $C_{\mathrm{loc}}^{0,1}$-formulation of the strong cosmic censorship conjecture in a neighbourhood of subextremal Kerr.

arXiv commentv1: 16 pages, 2 figures; v2: 25 pages, 4 figures, significantly expanded version: examples added, more background and details, results unchanged. Version accepted for publication in Inventiones Mathematicae