Raychaudhuri equations and gravitational collapse in Einstein-Cartan theory

Understand

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.