Integration of the geodesic equations via Noether symmetries

Abstract

Through this paper, 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, Reïssner–Nordström and Kerr spacetimes. After obtaining the approximate Noether symmetries of the Schwarzschild, Reïssner–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 [Formula: see text].