The Energy of Regular Black Hole in General Relativity Coupled to Nonlinear Electrodynamics

Abstract

According to the Einstein, Weinberg, and M{\o}ller energy-momentum complexes, we evaluate the energy distribution of the singularity-free solution of the Einstein field equations coupled to a suitable nonlinear electrodynamics suggested by Ay\'{o}n-Beato and Garc\'{i}a. The results show that the energy associated with the definitions of Einstein and Weinberg are the same, but M{\o}ller not. Using the power series expansion, we find out that the first two terms in the expression are the same as the energy distributions of the Reissner-Nordstr\"{o}m solution, and the third term could be used to survey the factualness between numerous solutions of the Einstein field eqautions coupled to a nonlinear electrodynamics.