Einstein and Møller energies of a particular asymptotically Reissner–Nordström non-singular black hole solution

Abstract

The localization of energy-momentum for a four-dimensional charged, static, and spherically symmetric, non-singular black hole solution that asymptotically behaves as a Reissner–Nordström solution, is studied. The space–time geometry is distinguished by a particular distribution function entering the mass function m(r). The non-singular character of the metric is warranted by the coupling of general relativity with a non-linear electrodynamics, whereby the resulting electric field is everywhere non-singular and asymptotically tends to the Maxwell field. The energy and momentum distributions are computed by applying the Einstein and Møller energy-momentum complexes. It is found that all the momenta vanish, while the energies depend on the electric charge, the mass, and the radial coordinate. Finally, the behavior of the energies near the origin, near infinity, as well as in the case of a vanishing electric charge is examined. © 2021 Wiley-VCH GmbH