Integration of the geodesic equations via Noether Symmetries

Abstract

Through this article, I will overview the use of Noether symmetry approach in discussing the integration of geodesic equations for the geodesic Lagrangians of spacetimes. I will also give some examples to reveal the efficiency of Noether symmetry approach by finding the first integrals related for the geodesic Lagrangians of the Gödel-type, Schwarzschild, Reissner-Nordström and Kerr spacetimes. After obtaining the approximate Noether symmetries of the Schwarzschild, Reissner-Nordström and Kerr spacetimes, the first integrals associated with each of approximate Noether symmetries have been integrated to find a general solution of geodesic equations in terms of the arc length $s$.

arXiv comment13 pages, no figures

References in corpus (6)

• Lie and Noether symmetries of geodesic equations and collineations
• Symmetries of geodesic motion in Gödel-type spacetimes
• Approximate Noether Symmetries of the Geodesic Equations for the Charged-Kerr Spacetime and Rescaling of Energy
• Approximate Noether gauge symmetries of Bardeen model
• A Proposal for Determining the Energy Content of Gravitational Waves by Using Approximate Symmetries of Differential Equations
• Approximate Noether Symmetries from Lagrangian for Plane Symmetric Spacetimes

Cited by in corpus (2)

• Hamilton-Jacobi and Klein-Gordon-Fock equations for a charged test particle in space-time with simply transitive four-parameter groups of motions
• Solutions of Maxwell equations for admissible electromagnetic fields, in spaces with simply transitive four-parameter groups of motions