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We numerically compute the renormalized expectation value$\langle\hat{\Phi}^{2}\rangle_{ren}$ of a minimally-coupled massless quantumscalar field in the interior of a four-dimensional Reissner-Nordstrom blackhole, in both the Hartle-Hawking and Unruh states. To this end we use arecently developed mode-sum renormalization scheme based on covariant pointsplitting. In both quantum states, $\langle\hat{\Phi}^{2}\rangle_{ren}$ isfound to approach a \emph{finite} value at the inner horizon (IH). The finalapproach to the IH asymptotic value is marked by an inverse-power tail$r_{*}^{-n}$, where $r_{*}$ is the Regge-Wheeler "tortoise coordinate", andwith $n=2$ for the Hartle-Hawking state and $n=3$ for the Unruh state. We alsoreport here the results of an analytical computation of these inverse-powertails of $\langle\hat{\Phi}^{2}\rangle_{ren}$ near the IH. Our numericalresults show very good agreement with this analytical derivation (for both thepower index and the tail amplitude), in both quantum states. Finally, from thisasymptotic behavior of $\langle\hat{\Phi}^{2}\rangle_{ren}$ we analyticallycompute the leading-order asymptotic behavior of the trace$\langle\hat{T}_{\mu}^{\mu}\rangle_{ren}$ of the renormalized stress-energytensor 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 knownparameter $b$). To the best of our knowledge, this is the firstfully-quantitative derivation of the asymptotic behavior of these renormalizedquantities at the inner horizon of a four-dimensional Reissner-Nordstrom blackhole.

Analysis of quantum effects inside spherical charged black holes