  To observe the dynamic formation of black holes in general relativity, one
essentially needs to prove that closed trapped surfaces form during evolution
from initial data that do not already contain trapped surfaces. We discuss the
recent development of the construction of such admissible initial data for
matter models. In addition, we extend known results for the Einstein equations
coupled to perfect fluids in spherical symmetry and with linear equation of
state to unbounded domains. Polytropic equations of state and regularity issues
with the direct application of the singularity theorems in general relativity
are discussed briefly.
