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

Understand

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.