A metric for gravitational collapse of dust around a Schwarzschild black
  hole
  We consider the problem of gravitational collapse of a fluid under the effect
of a Schwarzschild black hole (e.g. a primordial one) that suddenly forms
inside the fluid. We assume the fluid initially be a uniform dust. Starting
from this configuration we obtain a class of metrics under some assumptions. We
find that the metric we obtain includes the dust collapse as a subcase. After
discussing some basic properties of the solution, we discuss the case of dust
collapse in more detail. We find that the radial and tangential pressures
outside the horizon may take positive or negative values depending on the
values of the parameters.
