  We numerically investigate the interior of a four-dimensional, asymptotically
flat, spherically symmetric charged black hole perturbed by a scalar field
$\Phi$. Previous study by Marolf and Ori indicated that late infalling
observers will encounter an effective shock wave as they approach the left
portion of the inner horizon. This shock manifests itself as a sudden change in
the values of various fields, within a tremendously short interval of proper
time $\tau$ of the infalling observers. We confirm this prediction numerically
for both test and self-gravitating scalar field perturbations. In both cases we
demonstrate the effective shock in the scalar field by exploring $\Phi(\tau)$
along a family of infalling timelike geodesics. In the self-gravitating case we
also demonstrate the shock in the area coordinate $r$ by exploring $r(\tau)$.
We confirm the theoretical prediction concerning the shock sharpening rate,
which is exponential in the time of infall into the black hole. In addition we
numerically probe the early stages of shock formation. We also employ a family
of null (rather than timelike) ingoing geodesics to probe the shock in $r$. We
use a finite-difference numerical code with double-null coordinates combined
with a recently developed adaptive gauge method in order to solve the (Einstein
+ scalar) field equations and to evolve the spacetime (and scalar field) $ - $
from the region outside the black hole down to the vicinity of the Cauchy
horizon and the spacelike $r=0$ singularity.
