The geometric nature of approximate Noether gauge symmetries

Abstract

We find the geometrical set of equations corresponding to the approximate Noether gauge symmetry conditions of the perturbed geodesic Lagrangian for spacetimes. Using the obtained new set of approximate Noether symmetry equations which involves exact, first-order and second-order metrics, we calculate exact, first-order and second-order approximate Noether gauge symmetry vectors of the geodesic Lagrangian for the potential function defining the dynamical system in spacetimes. We apply our geometrical method to each of the Schwarzschild metric and Reissner–Nordstrom metric.