• Conservation laws and solution of the geodesic system of Gödel’s metric via Lie and Noether symmetries

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    • Keywords


      Geodesic equations; Lie symmetries; Noether symmetries; isometries.

    • 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.

    • Author Affiliations



      1. General Directorate of Education of A’ddakhiliyah Province, Ministry of Education, Sultanate of Oman
      2. School of Mathematics, University of the Witwatersrand, Johannesburg, South Africa
    • Dates

  • Pramana – Journal of Physics | News

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      Posted on July 25, 2019

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