  A new class of solutions of the Einstein field equations in spherical
symmetry is found. The new solutions are mathematically described as the
metrics admitting separation of variables in area-radius coordinates.
Physically, they describe the gravitational collapse of a class of anisotropic
elastic materials. Standard requirements of physical acceptability are
satisfied, in particular, existence of an equation of state in closed form,
weak energy condition, and existence of a regular Cauchy surface at which the
collapse begins. The matter properties are generic in the sense that both the
radial and the tangential stresses are non vanishing, and the kinematical
properties are generic as well, since shear, expansion, and acceleration are
also non-vanishing. As a test-bed for cosmic censorship, the nature of the
future singularity forming at the center is analyzed as an existence problem
for o.d.e. at a singular point using techniques based on comparison theorems,
and the spectrum of endstates - blackholes or naked singularities - is found in
full generality. Consequences of these results on the Cosmic Censorship
conjecture are discussed.
