Articles written in Pramana – Journal of Physics
Volume 96 All articles Published: 23 June 2022 Article ID 0121 Research Article
Conservation laws and solution of the geodesic system of Gödel’s metric via Lie and Noether symmetries
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.
Volume 97, 2023
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