  The full computation of the renormalized expectation values
$\langle\Phi^{2}\rangle_{ren}$ and $\langle\hat{T}_{\mu\nu}\rangle_{ren}$ in 4D
black hole interiors has been a long standing challenge, which has impeded the
investigation of quantum effects on the internal structure of black holes for
decades. Employing a recently developed mode sum renormalization scheme to
numerically implement the point-splitting method, we report here the first
computation of $\langle\Phi^{2}\rangle_{ren}$ in Unruh state in the region
inside the event horizon of a 4D Schwarzschild black hole. We further present
its Hartle-Hawking counterpart, which we calculated using the same method, and
obtain a fairly good agreement with previous results attained using an entirely
different method by Candelas and Jensen in 1986. Our results further agree upon
approaching the event horizon when compared with previous results calculated
outside the black hole. Finally, the results we obtained for Hartle-Hawking
state at the event horizon agree with previous analytical results published by
Candelas in 1980. This work sets the stage for further explorations of
$\langle\Phi^{2}\rangle_{ren}$ and $\langle\hat{T}_{\mu\nu}\rangle_{ren}$ in 4D
black hole interiors.
