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). Invari...

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Bibliographic Details
Published in:Pramāṇa 2022-09, Vol.96 (3), Article 121
Main Authors: AlKindi, F, Kara, A H, Ziad, M
Format: Article
Language:English
Subjects:
Astronomy
Astrophysics and Astroparticles
Observations and Techniques
Physics
Physics and Astronomy
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Summary: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.
ISSN:0973-7111
0973-7111
DOI:10.1007/s12043-022-02361-8