Raychaudhuri equations and gravitational collapse in Einstein-Cartan theory

TL;DR

This paper extends Raychaudhuri equations to spacetimes with torsion in Einstein-Cartan theory, derives effective stress-energy tensors, and suggests torsion could prevent singularities during gravitational collapse.

Contribution

It generalizes Raychaudhuri equations to include torsion and explores how intrinsic spin and torsion influence gravitational collapse and singularity avoidance.

Findings

Null energy condition violated before Planck density

Torsion may prevent spacetime singularities

Effective stress-energy tensor derived in Einstein-Cartan theory

Abstract

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.