  We numerically compute the renormalized expectation value
$\langle\hat{\Phi}^{2}\rangle_{ren}$ of a minimally-coupled massless quantum
scalar field in the interior of a four-dimensional Reissner-Nordstrom black
hole, in both the Hartle-Hawking and Unruh states. To this end we use a
recently developed mode-sum renormalization scheme based on covariant point
splitting. In both quantum states, $\langle\hat{\Phi}^{2}\rangle_{ren}$ is
found to approach a \emph{finite} value at the inner horizon (IH). The final
approach to the IH asymptotic value is marked by an inverse-power tail
$r_{*}^{-n}$, where $r_{*}$ is the Regge-Wheeler "tortoise coordinate", and
with $n=2$ for the Hartle-Hawking state and $n=3$ for the Unruh state. We also
report here the results of an analytical computation of these inverse-power
tails of $\langle\hat{\Phi}^{2}\rangle_{ren}$ near the IH. Our numerical
results show very good agreement with this analytical derivation (for both the
power index and the tail amplitude), in both quantum states. Finally, from this
asymptotic behavior of $\langle\hat{\Phi}^{2}\rangle_{ren}$ we analytically
compute the leading-order asymptotic behavior of the trace
$\langle\hat{T}_{\mu}^{\mu}\rangle_{ren}$ of the renormalized stress-energy
tensor at the IH. In both quantum states this quantity is found to diverge like
$b(r-r_{-})^{-1}r_{*}^{-n-2}$ (with $n$ specified above, and with a known
parameter $b$). To the best of our knowledge, this is the first
fully-quantitative derivation of the asymptotic behavior of these renormalized
quantities at the inner horizon of a four-dimensional Reissner-Nordstrom black
hole.
