Energy distribution of a regular black hole solution in Einstein-nonlinear electrodynamics

Abstract

In this work a study about the energy-momentum of a new four-dimensional spherically symmetric, static and charged, regular black hole solution developed in the context of general relativity coupled to nonlinear electrodynamics is presented. Asymptotically, this new black hole solution behaves as the Reissner-Nordstr\"om solution only for the particular value {\mu}=4, where {\mu} is a positive integer parameter appearing in the mass function of the solution. The calculations are performed by use of the Einstein, Landau-Lifshitz, Weinberg and M{\o}ller energy-momentum complexes. In all the aforesaid prescriptions, the expressions for the energy of the gravitating system considered depend on the mass M of the black hole, its charge q, a positive integer {\alpha} and the radial coordinate r. In all these pseudotensorial prescriptions the momenta are found to vanish, while the Landau-Lifshitz and Weinberg prescriptions give the same result for the energy distribution. In addition, the limiting behavior of the energy for the cases r tends toward infinity, r=0 and q=0 is studied. The special case {\mu}=4 and {\alpha}=3 is also examined. We conclude that the Einstein and M{\o}ller energy-momentum complexes can be considered as the most reliable tools for the study of the energy-momentum localization of a gravitating system.