Raychaudhuri and optical equations for null geodesic congruences with torsion

Abstract

We study null geodesic congruences (NGCs) in the presence of spacetime torsion, recovering and extending results in the literature. Only the highest spin irreducible component of torsion gives a proper acceleration with respect to metric NGCs, but at the same time obstructs abreastness of the geodesics. This means that it is necessary to follow the evolution of the drift term in the optical equations, and not just shear, twist and expansion. We show how the optical equations depend on the non-Riemannian components of the curvature, and how they reduce to the metric ones when the highest spin component of torsion vanishes.

v2: improved text, a few equations and a subsection added. v3: typo in one equation corrected, improved conclusions and other minor amendments

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• Einstein manifolds with torsion and nonmetricity
• Static compact objects in Einstein-Cartan theory
• Cosmological signatures of torsion and how to distinguish torsion from the dark sector
• Super-entropic black hole with Immirzi hair
• Raychaudhuri equations and gravitational collapse in Einstein-Cartan theory
• Kinematics in Metric-Affine Geometry
• The Uplifting of AdS Type to Quintessence Like Potential Induced by Frozen Large Scale Lorentz Violation
• Symmetries and conserved quantities with arbitrary torsion: A generalization of Killing's theorem
• Canonical structure of minimal varying $\Lambda$ theories
• Lagrangian Formulation of the Raychaudhuri Equation in Non-Riemannian Geometry
• Testing the null energy condition with precise distance measurements
• Tidal heating in a Riemann-Cartan spacetime
• On the Stability of a Wormhole in the Maximally-Extended Reissner-Nordström Solution