Lagrangian Formulation of the Raychaudhuri Equation in Non-Riemannian Geometry

Abstract

The Raychaudhuri equation for a congruence of curves in a general non-Riemannian geometry is derived. A formal connection is established between the expansion scalar and the cross-sectional volume of the congruence. It is found that the expansion scalar is equal to the fractional rate of change of volume, weighted by a scalar factor that depends on the non-Riemannian features of the geometry. Treating the congruence of curves as a dynamical system, an appropriate Lagrangian is derived such that the corresponding Euler-Lagrange equation is the Raychaudhuri equation. A Hamiltonian formulation and Poisson brackets are also presented.

Accepted for publication in Int. J Geom. Meth. Mod. Phys

References in corpus (12)

• The teleparallel equivalent of general relativity
• Teleparallel Gravity: From Theory to Cosmology
• The Raychaudhuri equations: a brief review
• Comparing Equivalent Gravities: common features and differences
• Geodesic deviation, Raychaudhuri equation, Newtonian limit, and tidal forces in Weyl-type $f(Q,T)$ gravity
• Spacetime thermodynamics in the presence of torsion
• Raychaudhuri equation in spacetimes with torsion
• The $3+1$ Formalism in the Geometric Trinity of Gravity
• Effect of Spin-Torsion Interaction on Raychaudhuri Equation
• Raychaudhuri equations and gravitational collapse in Einstein-Cartan theory
• Kinematics and dynamics of null hypersurfaces in the Einstein-Cartan spacetime and related thermodynamic interpretation
• Kinematics in Metric-Affine Geometry

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