Abstract
We consider the geodesic system for Gödel’s metric as a toy model and solve it analytically using its Lie point symmetries. It is shown that the differential invariants of these symmetries reduce the second-order non-linear system to a single second-order ordinary differential equation (ODE). Invariance of the latter under a one-dimensional Lie point symmetry group reduces it to an integrable first-order ODE. A complete solution of the system is then achieved. The sub-algebras of Noether symmetries and isometries are then found with their corresponding first integrals.
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AlKindi, F., Kara, A.H. & Ziad, M. Conservation laws and solution of the geodesic system of Gödel’s metric via Lie and Noether symmetries. Pramana - J Phys 96, 121 (2022). https://doi.org/10.1007/s12043-022-02361-8
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DOI: https://doi.org/10.1007/s12043-022-02361-8