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- Title
Lagrangian formulation of the Raychaudhuri equation in non-Riemannian geometry.
- Authors
Agashe, Anish
- Abstract
The Raychaudhuri equation (RE) 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 RE. A Hamiltonian formulation and Poisson brackets are also presented.
- Subjects
EULER-Lagrange equations; POISSON brackets; GEOMETRY; LAGRANGE equations; EQUATIONS; RIEMANNIAN geometry
- Publication
International Journal of Geometric Methods in Modern Physics, 2024, Vol 21, Issue 6, p1
- ISSN
0219-8878
- Publication type
Article
- DOI
10.1142/S0219887824501202