On the cosmic censorship conjecture for spherically symmetric, shear-free perfect fluid spacetimes

With the aim of testing the cosmic censorship conjecture for perfect fluid spacetimes, two classes of spherically symmetric perfect fluid solutions ob eying the shear-free condition are examined. The final end states of gravit ational collapse can be investigated analytically for such solutions, and i t is shown that homogeneous configurations always form black holes. This pr operty also holds true for inhomogeneous solutions provided that the collap se occurs in a synchronous manner.