Localization of Energy and Momentum in an Asymptotically Reissner-Nordstr\"om Non-singular Black Hole Space-time Geometry
Abstract
The space-time geometry exterior to a new four-dimensional, spherically symmetric and charged black hole solution that, through a coupling of general relativity with a non-linear electrodynamics, is everywhere non-singular, for small r it behaves as a de Sitter metric, and asymptotically it behaves as the Reissner-Nordstr\"om metric, is considered in order to study the energy-momentum localization. For the calculation of the energy and momentum distributions, the Einstein, Landau-Lifshitz, Weinberg and M ller energy-momentum complexes have been applied. The results obtained show that in all prescriptions the energy depends on the mass M of the black hole, the charge q, two parameters % a∈ Z+ and γ∈ R+, and on the radial coordinate r. The calculations performed in each prescription show that all the momenta vanish. Additionally, some limiting and particular cases for r and q are studied, and a possible connection with strong gravitational lensing and micro lensing is attempted.