  Rotating and/or charged black hole spacetimes possess a Cauchy horizon,
beyond which Einstein's equations of General Relativity cease to be
deterministic. This led to the formulation of the Strong Cosmic Censorship
conjecture that such horizons become irregular under field perturbations. We
consider linear field perturbations of rotating and electrically-charged
(Kerr-Newman-de Sitter) black holes in a universe with a positive cosmological
constant. By calculating the quasinormal modes for scalar and fermion fields,
we provide evidence for the existence of weak solutions to Einstein's equations
across the Cauchy horizon in the nearly-extremal regime. We thus provide, for
the first time, evidence for violation of Strong Cosmic Censorship in
(4-dimensional) rotating black hole spacetimes.
