Lipschitz inextendibility of weak null singularities from curvature blow-up

TL;DR

This paper proves that weak null singularities in rotating black holes cannot be extended in a Lipschitz continuous manner, using a new curvature blow-up approach, which advances understanding of cosmic censorship.

Contribution

Introduces a novel method linking curvature blow-up to $C^{0,1}_{ ext{loc}}$-inextendibility without symmetry assumptions, impacting the strong cosmic censorship conjecture.

Findings

Weak null singularities are $C^{0,1}_{ ext{loc}}$-inextendible due to curvature blow-up.

New proof strategy does not rely on symmetry assumptions.

Results are relevant for the interior of generic rotating black holes.

Abstract

We prove the $C^{0,1}_{\mathrm{loc}}$-inextendibility of weak null singularities without any symmetry assumptions. The proof introduces a new strategy to infer $C^{0,1}_{\mathrm{loc}}$-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 $C^{0,1}_{\mathrm{loc}}$-formulation of the strong cosmic censorship conjecture in a neighbourhood of subextremal Kerr.