Energy of Bardeen Model Using Approximate Symmetry Method

TL;DR

This paper applies approximate symmetry methods to the Bardeen black hole model in general relativity, revealing that energy calculations require a re-scaling factor at third-order approximation, offering new insights into energy definitions.

Contribution

It introduces a third-order approximate symmetry approach to evaluate energy in the Bardeen black hole model, highlighting the necessity of re-scaling energy in higher-order approximations.

Findings

Energy must be re-scaled at third-order approximation

Approximate Lie symmetry methods are effective for energy analysis

Re-scaling factor provides new insights into energy in regular black holes

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 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 of this re-scaling factor.