Localization of Energy and Momentum in an Asymptotically Reissner-Nordström Non-Singular Black Hole Space-Time Geometry

Irina Radinschi,Pradyumn Kumar Sahoo,Theophanes Grammenos,Surajit Chattopadhyay,Marius-Mihai Cazacu

doi:10.3390/universe6050069

Irina Radinschi, Pradyumn Kumar Sahoo + Show 3 more

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https://doi.org/10.3390/universe6050069

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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 non-singular everywhere, 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 energy-momentum localization. For the calculation of the energy and momentum distributions, the Einstein, Landau-Lifshitz, Weinberg and Møller 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.

Highlights

The problem of energy-momentum localization, being one of the most challenging problems in classical general relativity in the search of a physically meaningful expression for the energy-momentum of the gravitational field, has triggered a lot of interesting research work, but still remains open and rather not fully understood
The results of the present paper come to support the use of the Einstein, Landau-Lifshitz, Weinberg and Møller energy-momentum complexes for the evaluation of the energy of a space-time geometry, while keeping in mind that the positive energy region serves as a convergent lens and the negative one as a divergent lens [60]
The study of the asymptotically Reissner-Nordström non-singular black hole space-time geometry could be of great importance for black hole physics, as it would allow testing this particular black hole, the best approach for this being gravitational lensing

Summary

Introduction

The problem of energy-momentum localization, being one of the most challenging problems in classical general relativity in the search of a physically meaningful expression for the energy-momentum of the gravitational field, has triggered a lot of interesting research work, but still remains open and rather not fully understood. Equations (15)–(17) the expression for the energy distribution in the Einstein prescription for the non-singular and charged black hole space-time that asymptotically behaves as the Reissner-Nordström solution is given by EE = M

Results

Conclusion