  Adapting and extending the techniques developed in recent work with Vasy for
the study of the Cauchy horizon of cosmological spacetimes, we obtain
boundedness, regularity and decay of linear scalar waves on subextremal
Reissner-Nordstr\"om and (slowly rotating) Kerr spacetimes, without any
symmetry assumptions; in particular, we provide simple microlocal and
scattering theoretic proofs of analogous results by Franzen. We show polynomial
decay of linear waves relative to a Sobolev space of order slightly above
$1/2$. This complements the generic $H^1_{\mathrm{loc}}$ blow-up result of Luk
and Oh.
