Approximate Symmetries and Approximate Conservation Laws for the Reissner-Nordstrom metric

Abstract:
Symmetries are very useful because they give conservation laws through Noether’s theorem. The system of geodesic equations inherits the symmetries of the manifold. Sometimes a manifold does not have exact symmetries but only has approximate symmetries. These approximate symmetries of manifolds can give us useful information. Here we define the approximate symmetries in the context of differential equations. Following the use of approximate symmetries by Kara, Mahomed and Qadir on the approximate symmetries of the Schwarzschild spacetime we have investigated the exact and approximate symmetries of the system of geodesic equations for Reissner-Nordstrom spacetime. For this purpose we need to formulate and use second order approximate symmetries. The corresponding approximate conservation laws are then discussed.