  It has been argued that the strong cosmic censorship conjecture is violated
by Reissner-Nordstr\"om-de Sitter black holes: for near-extremal black holes,
generic scalar field perturbations arising from smooth initial data have finite
energy at the Cauchy horizon even though they are not continuously
differentiable there. In this paper, we consider the analogous problem for
coupled gravitational and electromagnetic perturbations. We find that such
perturbations exhibit a much worse violation of strong cosmic censorship: for a
sufficiently large near-extremal black hole, perturbations arising from smooth
initial data can be extended through the Cauchy horizon in an arbitrarily
smooth way. This is in apparent contradiction with an old argument in favour of
strong cosmic censorship. We resolve this contradiction by showing that this
old argument is valid only for initial data that is not smooth. This is in
agreement with the recent proposal that, to recover strong cosmic censorship,
one must allow rough initial data.
