  Motivated by the Strong Cosmic Censorship Conjecture in the presence of
matter, we study the Einstein equations coupled with a charged/massive scalar
field with spherically symmetric characteristic data relaxing to a
Reissner-Nordstr\"om event horizon. Contrary to the vacuum case, the relaxation
rate is conjectured to be slow (non-integrable), opening the possibility that
the matter fields and the metric coefficients blow up in amplitude at the
Cauchy horizon, not just in energy. We show that whether this blow-up in
amplitude occurs or not depends on a novel oscillation condition on the event
horizon which determines whether or not a resonance is excited dynamically. If
the oscillation condition is satisfied, then the resonance is not excited and
we show boundedness and continuous extendibility of the matter fields and the
metric across the Cauchy horizon. If the oscillation condition is violated,
then by the combined effect of slow decay and the resonance being excited, we
show that the massive uncharged scalar field blows up in amplitude. In our
companion paper, we show that in the latter case a novel null contraction
singularity forms at the Cauchy horizon, across which the metric is not
continuously extendible in the usual sense. Heuristic arguments in the physics
literature indicate that the oscillation condition should be satisfied
generically on the event horizon. If these heuristics are true, then our result
falsifies the $C^0$-formulation of Strong Cosmic Censorship by means of
oscillations.
