  We explore the fate of matter falling into a macroscopic Schwarzschild black
hole for the simplified case of a radially collapsing thin spherical shell for
which the back reaction of the geometry can be neglected. We treat the internal
dynamics of the infalling matter in the framework of viscous relativistic
hydrodynamics and calculate how the internal temperature of the collapsing
matter evolves as it falls toward the Schwarzschild singularity. We find that
viscous hydrodynamics fails when either, the dissipative radial pressure
exceeds the thermal pressure and the total radial pressure becomes negative, or
the time scale of variation of the tidal forces acting on the collapsing matter
becomes shorter than the characteristic hydrodynamic response time.
