Raychaudhuri equations and gravitational collapse 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.

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• Non-Affine Extensions of the Raychaudhuri Equation in the K-essence Framework
• Evolution of the early universe in Einstein-Cartan theory
• Lagrangian Formulation of the Raychaudhuri Equation in Non-Riemannian Geometry
• Tidal heating in a Riemann-Cartan spacetime
• Exploring Cosmological Implications of the Modified Raychaudhuri Equation in Non-Gravitating Vacuum Energy Theory
• Possible fluid interpretation and tidal force equation on a generic null hypersurface in Einstein-Cartan theory
• Torsional four-fermion interaction and the Raychaudhuri equation
• From Geometry to Observation: Gravitational Waves and the Raychaudhuri Equation