The interior of dynamical vacuum black holes I: The $C^0$-stability of the Kerr Cauchy horizon

TL;DR

This paper proves that the interior of rotating vacuum black holes can be extended continuously across the Cauchy horizon, challenging the strong cosmic censorship conjecture and suggesting the presence of weak null singularities.

Contribution

It establishes the $C^0$-stability of the Kerr Cauchy horizon starting from interior data, advancing understanding of black hole interiors without symmetry assumptions.

Findings

Maximal Cauchy evolution extends across the Cauchy horizon as a continuous metric.

The results imply potential inextendibility in stronger regularity classes.

Supports the idea that weak null singularities are generically present inside black holes.

Abstract

We initiate a series of works where we study the interior of dynamical rotating vacuum black holes without symmetry. In the present paper, we take up the problem starting from appropriate Cauchy data for the Einstein vacuum equations defined on a hypersurface already within the black hole interior, representing the expected geometry just inside the event horizon. We prove that for all such data, the maximal Cauchy evolution can be extended across a non-trivial piece of Cauchy horizon as a Lorentzian manifold with continuous metric. In subsequent work, we will retrieve our assumptions on data assuming only that the black hole event horizon geometry suitably asymptotes to a rotating Kerr solution. In particular, if the exterior region of the Kerr family is proven to be dynamically stable---as is widely expected---then it will follow that the $C^0$-inextendibility formulation of Penrose's celebrated strong cosmic censorship conjecture is in fact false. The proof suggests, however, that the $C^0$-metric Cauchy horizons thus arising are generically singular in an essential way, representing so-called "weak null singularities", and thus that a revised version of strong cosmic censorship holds.