  The Raychaudhuri equations for the expansion, shear and vorticity are
generalized in a spacetime with torsion for timelike as well as null
congruences. These equations are purely geometrical like the original
Raychaudhuri equations and could be reduced to them when there is no torsion.
Using the Einstein-Cartan-Sciama-Kibble field equations the effective
stress-energy tensor is derived. We also consider an Oppenheimer-Snyder model
for the gravitational collapse of dust. It is shown that the null energy
condition (NEC) is violated before the density of the collapsing dust reaches
the Planck density, hinting that the spacetime singularity may be avoided if
there is a non-zero torsion,i.e. if the collapsing dust particles possess
intrinsic spin.
