Energy of the Bardeen model using an approximate symmetry method

Abstract

In this paper, we investigate the energy problem in general relativity using approximate Lie symmetry methods for differential equations. This procedure is applied to the Bardeen model (the regular black-hole solution). Here, we are forced to evaluate the third-order approximate symmetries of the orbital and geodesic equations. It is shown that energy must be re-scaled by some factor in the third-order approximation. We discuss the insights into this re-scaling factor.