Lagrangian Formulation of the Raychaudhuri Equation in Non-Riemannian Geometry
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arXiv
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| Format: | Preprint |
| Published: |
2023
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| _version_ | 1866911918807056384 |
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| author | Agashe, Anish |
| author_facet | Agashe, Anish |
| contents | 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. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2312_06418 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Lagrangian Formulation of the Raychaudhuri Equation in Non-Riemannian Geometry Agashe, Anish General Relativity and Quantum Cosmology Mathematical Physics Differential Geometry 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. |
| title | Lagrangian Formulation of the Raychaudhuri Equation in Non-Riemannian Geometry |
| topic | General Relativity and Quantum Cosmology Mathematical Physics Differential Geometry |
| url | https://arxiv.org/abs/2312.06418 |