Energy-momentum for a charged nonsingular black hole solution with a nonlinear mass function

TL;DR

This paper investigates the energy-momentum distribution of a novel charged, nonsingular black hole solution in general relativity with nonlinear electrodynamics, analyzing various energy-momentum complexes and their limiting behaviors.

Contribution

It introduces a new black hole solution with a nonlinear mass function inspired by logistic distribution and compares energy-momentum distributions across multiple prescriptions.

Findings

Energy distribution depends on mass, charge, parameter β, and radial distance.

Landau-Lifshitz and Weinberg prescriptions give identical energy results.

All momenta vanish in the studied prescriptions.

Abstract

The energy-momentum of a new four-dimensional, charged, spherically symmetric and nonsingular black hole solution constructed in the context of general relativity coupled to a theory of nonlinear electrodynamics is investigated, whereby the nonlinear mass function is inspired by the probability density function of the continuous logistic distribution. The energy and momentum distributions are calculated by use of the Einstein, Landau-Lifshitz, Weinberg and M{\o}ller energy-momentum complexes. In all these prescriptions it is found that the energy distribution depends on the mass $M$ and the charge $q$ of the black hole, an additional parameter $\beta$ coming from the gravitational background considered, and on the radial coordinate $r$. Further, the Landau-Lifshitz and Weinberg prescriptions yield the same result for the energy, while in all the aforesaid prescriptions all the momenta vanish. We also focus on the study of the limiting behavior of the energy for different values of the radial coordinate, the parameter $\beta$, and the charge $q$. Finally, it is pointed out that for $r\rightarrow \infty$ and $q = 0$ all the energy-momentum complexes yield the same expression for the energy distribution as in the case of the Schwarzschild black hole solution.