of this model (homogeneity, sphericity, dust equation of state) are relaxed. However, we now know that this is not so.

When the assumption of homogeneity is relaxed, there is an exact solution of Einstein equations - the Datt-Tolman-Bondi solution, which describes collapse of a dust sphere with non-uniform initial density. Two kinds of singularities can result - shell crossing and shell focusing. While the former have a Newtonian analog, at least some of the latter appear to be of purely relativistic origin. It has been shown by various authors [@dust] that the shell-focusing singularities can be of both the black hole and naked type, depending on the initial conditions.

As an illustration, we mention the following interesting case. Consider the collapse of a dust sphere, starting from rest, and having an initial density profile near the center given by $$\rho (R) = \rho_{0}  +  \rho_{1}R  +  {1\over 2} \rho_{2} R^{2}
   +  {1\over 6} \rho_{3} R^{3} + ....$$ It turns out that the singularity is naked if $\rho_{1}$ is less than zero, and also if $\rho_{1}$ is equal to zero and $\rho_{2}$ is less than zero. If both $\rho_{1}$ and $\rho_{2}$ are zero and $\rho_{3}$ is negative, then we define a 