Localization of Energy and Momentum in an Asymptotically Reissner-Nordström 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-Nordström 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 Møller 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 and $\gamma \in {\mathbb{R}}^{+}$, 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.

To appear in Universe