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arXiv · 2312.06418

Lagrangian Formulation of the Raychaudhuri Equation in Non-Riemannian Geometry

Anish Agashe
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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.

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Anish Agashe. 2023-12-11. Lagrangian Formulation of the Raychaudhuri Equation in Non-Riemannian Geometry. https://doi.org/10.1142/s0219887824501202

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