Energy-Momentum for a Charged Nonsingular Black Hole Solution with a Nonlinear Mass Function

Irina Radinschi,Sayeedul Islam,Andromahi Spanou,Theophanes Grammenos,Antonio Pasqua,Surajit Chattopadhyay,Farook Rahaman

doi:10.1155/2017/7656389

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 Møller 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 β coming from the gravitational background considered, and 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 β, and the charge q. Finally, it is pointed out that, for r→∞ 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.

Highlights

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
It is found that the energy distribution depends on the mass M and the charge q of the black hole, an additional parameter β coming from the gravitational background considered, and the radial coordinate r
We focus on the study of the limiting behavior of the energy for different values of the radial coordinate, the parameter β, and the charge q

Summary

Introduction

The problem of the energy-momentum localization in general relativity has been investigated over the years by using various and different powerful tools such as superenergy tensors [1,2,3,4], quasilocal expressions [5,6,7,8,9], and the mostly known pseudotensorial energy-momentum complexes introduced by Einstein [10, 11], Landau and Lifshitz [12], Papapetrou [13], Bergmann and Thomson [14], Møller [15], Weinberg [16], and Qadir and Sharif [17].As it is well-known, the main difficulty which arises consists in developing a properly defined expression for the energy density of the gravitational background. In what follows, we are going to investigate the problem of energy-momentum localization for a charged and nonsingular black hole solution with the space-time described by (1), (4) and the nonlinear mass function: β

Results

Conclusion