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

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