Localization of Energy and Momentum in an Asymptotically Reissner-Nordström Non-Singular Black Hole Space-Time Geometry
2020
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 non-singular everywhere, for small r it behaves as a de Sitter metric, and asymptotically it behaves as the Reissner-Nordstrom metric, is considered in order to study energy-momentum localization. For the calculation of the energy and momentum distributions, the Einstein, Landau-Lifshitz, Weinberg and Moller energy-momentum complexes were 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 microlensing is attempted.
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