  Following a program on black hole nonmodal linear stability initiated in
Phys.\ Rev.\ Lett.\ {\bf 112} (2014) 191101, we study odd linear perturbations
of the Einstein-Maxwell equations around a Reissner-Nordstr\"om (A)dS black
hole. We show that all the gauge invariant information in the metric and
Maxwell field perturbations is encoded in the spacetime scalars $\mathcal{F}
=\delta (F^*_{\alpha \beta} F^{\alpha \beta})$ and $\mathcal{Q} =\delta
(\tfrac{1}{48} C^*_{\alpha \beta \gamma \delta} C^{\alpha \beta \gamma
\delta})$, where $C_{\alpha \beta \gamma \delta}$ is the Weyl tensor,
$F_{\alpha \beta}$ the Maxwell field, a star denotes Hodge dual and $\delta$
means first order variation, and that the linearized Einstein-Maxwell equations
are equivalent to a coupled system of wave equations for $\mathcal{F}$ and
$\mathcal{Q}$. For nonnegative cosmological constant we prove that
$\mathcal{F}$ and $\mathcal{Q}$ are pointwise bounded on the outer static
region. The fields are shown to diverge as the Cauchy horizon is approached
from the inner dynamical region, providing evidence supporting strong cosmic
censorship. In the asymptotically AdS case the dynamics depends on the boundary
condition at the conformal timelike boundary and there are instabilities if
Robin boundary conditions are chosen.
