Second-Order Approximate Symmetries of the Geodesic Equations for the Reissner-Nordstr\"om Metric and Re-Scaling of Energy of a Test Particle

TL;DR

This paper investigates second-order approximate symmetries of geodesic equations in Reissner-Nordström spacetime, revealing that energy must be rescaled at this approximation level, with implications for understanding test particle dynamics.

Contribution

It extends the analysis of approximate symmetries to Reissner-Nordström spacetime using second-order approximations, showing energy rescaling is necessary.

Findings

Energy rescaling is required at second-order approximation.

Approximate symmetries help understand conserved quantities.

Implications for test particle energy in RN spacetime.

Abstract

Following the use of approximate symmetries for the Schwarzschild spacetime by A.H. Kara, F.M. Mahomed and A. Qadir (Nonlinear Dynam., to appear), we have investigated the exact and approximate symmetries of the system of geodesic equations for the Reissner-Nordstr\"om spacetime (RN). For this purpose we are forced to use second order approximate symmetries. It is shown that in the second-order approximation, energy must be rescaled for the RN metric. The implications of this rescaling are discussed.