Hawking-like radiation and the density matrix for an infalling observer
  during gravitational collapse
  We study time-dependant Hawking-like radiation as seen by an infalling
observer during gravitational collapse of a thin shell. We calculate the
occupation number of particles whose frequencies are measured in the proper
time of an infalling observer in Eddington-Finkelstein coordinates. We solve
the equations for the whole process from the beginning of the collapse till the
moment when the collapsing shell reaches zero radius. The radiation
distribution is not thermal in the whole frequency regime, but it is
approximately thermal for the wavelengths of the order of the Schwarzschild
radius of the collapsing shell. After the Schwarzschild radius is crossed, the
temperature increases without limits as the singularity is approached. We also
calculate the density matrix associated with this radiation. It turns out that
the off-diagonal correlation terms to the diagonal Hawking's leading order
terms are very important. While the trace of the diagonal (Hawking's) density
matrix squared decreases during the evolution, the trace of the total density
matrix squared remains unity at all times and all frequencies.
