  We have investigated the local invariant scalar observables - energy density
and flux - which explicitly depend on the kinematics of the concerned observers
in the Vaidya gravitational collapse geometry. The use of globally defined null
coordinates allows for the definition of a unique in-vacuum for the scalar
field propagating in this background. Computing the stress-energy tensor for
this scalar field, we work out the energy density and flux for the static
observers outside the horizon and then consider the radially in-falling
observers who fall in from some specified initial radius all the way through
the horizon and inside to the eventual singularity. Our results confirm the
thermal Tolman-shifted energy density and fluxes for the static observers which
diverge at the horizon. For the in-falling observer starting from far off, both
the quantities -- energy density and flux at the horizon crossing are
\emph{regular and finite}. For example, the flux at the horizon for the
in-falling observer from infinity is approximately 24 times the flux for the
observer at infinity. Compared with the static observers in the near-horizon
region, this is quite small. Both the quantities grow as the in-fall progresses
inside the horizon and diverge at the singularity.

General Relativity and Quantum Cosmology;High Energy Physics - Theory