  We solve the Klein-Gordon equation for a scalar field, in the background
geometry of a dust cloud collapsing to form a black hole, everywhere in the
(1+1) spacetime: that is, both inside and outside the event horizon and
arbitrarily close to the curvature singularity. This allows us to determine the
regularized stress tensor expectation value, everywhere in the appropriate
quantum state (viz., the Unruh vacuum) of the field. We use this to study the
behaviour of energy density and the flux measured in local inertial frames for
the radially freely falling observer at any given event. Outside the black
hole, energy density and flux lead to the standard results expected from the
Hawking radiation emanating from the black hole, as the collapse proceeds.
Inside the collapsing dust ball, the energy densities of both matter and scalar
field diverge near the singularity in both (1+1) and (1+3) spacetime
dimensions; but the energy density of the field dominates over that of
classical matter. In the (1+3) dimensions, the total energy (of both scalar
field and classical matter) inside a small spatial volume around the
singularity is finite (and goes to zero as the size of the region goes to zero)
but the total energy of the quantum field still dominates over that of the
classical matter. Inside the event horizon, but \textit{outside} the collapsing
matter, freely falling observers find that the energy density and the flux
diverge close to the singularity. In this region, even the integrated energy
inside a small spatial volume enclosing the singularity diverges. This result
holds in both (1+1) and (1+3) spacetime dimensions with a \emph{milder}
divergence for the total energy inside a small region in (1+3) dimensions.
These results suggest that the back-reaction effects are significant even in
the region \emph{outside the matter but inside the event horizon}, close to the
singularity.
