Research Article
Einstein and Møller Energy-Momentum Complexes for
a New Regular Black Hole Solution with a Nonlinear
Electrodynamics Source
Irina Radinschi,
1
Farook Rahaman,
2
Theophanes Grammenos,
3
and Sayeedul Islam
2
1
Department of Physics, Gh. Asachi Technical University, 700050 Iasi, Romania
2
Department of Mathematics, Jadavpur University, Kolkata, West Bengal 700 032, India
3
Department of Civil Engineering, University of Tessaly, 383 34 Volos, Greece
Correspondence should be addressed to Irina Radinschi; radinschi@yahoo.com
Received 9 June 2016; Accepted 15 September 2016
Academic Editor: Sally Seidel
Copyright © 2016 Irina Radinschi et al. Tis is an open access article distributed under the Creative Commons Attribution License,
which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. Te
publication of this article was funded by SCOAP
3
.
A study about the energy and momentum distributions of a new charged regular black hole solution with a nonlinear
electrodynamics source is presented. Te energy and momentum are calculated using the Einstein and Møller energy-momentum
complexes. Te results show that in both pseudotensorial prescriptions the expressions for the energy of the gravitational
background depend on the mass and the charge of the black hole, an additional factor coming from the spacetime metric
considered, and the radial coordinate , while in both prescriptions all the momenta vanish. Further, it is pointed out that in some
limiting and particular cases the two complexes yield the same expression for the energy distribution as that obtained in the relevant
literature for the Schwarzschild black hole solution.
1. Introduction
Energy-momentum localization plays a leading role in the
theories advanced over the years in relation to General
Relativity. Tere is a major difculty, however, in formulating
a proper defnition for the energy density of gravitational
backgrounds. Indeed, the key problem is the lack of a
satisfactory description for the gravitational energy.
Many researchers have conducted extensive research
using diferent methods for energy-momentum localization.
Standard research methods include the use of diferent tools,
such as super-energy tensors [1–4], quasilocal expressions [5–
9], and the famous energy-momentum complexes of Einstein
[10, 11], Landau and Lifshitz [12], Papapetrou [13], Bergmann
and Tomson [14], Møller [15], Weinberg [16], and Qadir and
Sharif [17]. Te main problem encountered is the dependence
on the reference frame of these pseudotensorial prescriptions.
An alternative method used in many studies on computing
the energy and momentum distributions in order to avoid
the dependence on coordinates is the teleparallel theory of
gravitation [18–26].
As regards pseudotensorial prescriptions, only the Møller
energy-momentum complex is a coordinate independent
tool. Schwarzschild Cartesian coordinates and Kerr-Schild
Cartesian coordinates are useful to compute the energy-
momentum in the case of the other pseudotensorial def-
initions. Over the past few decades, despite the criticism
directed against energy-momentum complexes concerning
mainly the physicalness of the results obtained by them, their
application has provided physically reasonable results for
many spacetime geometries, more particularly for geometries
in (3+1), (2+1), and (1+1) dimensions [27–58].
Tere is an agreement between the Einstein, Landau-
Lifshitz, Papapetrou, Bergmann-Tomson, Weinberg, and
Møller prescriptions, on the one hand, and the defnition
of the quasilocal mass advanced by Penrose [59] and devel-
oped by Tod [60] for some gravitating systems, on the
other hand (see [61] for a comprehensive review). Several
Hindawi Publishing Corporation
Advances in High Energy Physics
Volume 2016, Article ID 9049308, 9 pages
http://dx.doi.org/10.1155/2016/9049308