The Energy of Regular Black Hole in General Relativity Coupled to Nonlinear Electrodynamics

Abstract

According to the Einstein, Weinberg, and Møller energy-momentum complexes, we evaluate the energy distribution of the singularity-free solution of the Einstein field equations coupled to a suitable nonlinear electrodynamics suggested by Ayón-Beato and García. The results show that the energy associated with the definitions of Einstein and Weinberg are the same, but Møller not. Using the power series expansion, we find out that the first two terms in the expression are the same as the energy distributions of the Reissner-Nordström solution, and the third term could be used to survey the factualness between numerous solutions of the Einstein field equations coupled to a nonlinear electrodynamics.

Energy Distribution of a Regular Class of Exact Black Hole Solutions

“…The discussion will involve some particular cases obtained in function of two specific parameters α and β, which represent the dipole moment and the quadrupole moment, respectively and that appear in the expression of the electric field. In addition we present a study of some particular solutions connected with a previous work [91].…”

“…Moreover, for some particular range of the parameters the WEC energy condition is satisfied. Particular imposed values of these parameters determine a previous solution given by the authors [91]. The solution is given by…”

“…We compute the energy distribution of this class of solution with the Einstein, Weinberg and Møller definitions. We present the Einstein, Weinberg and Møller energy-momentum complexes [91] and the results obtained for the energy distributions. The energy component in the Einstein [1][2][3] prescription is given by…”

“…The connection between the energy component of the covariant energy-momentum four vector of the Weinberg energy-momentum complex and the energy in the Einstein prescription [91] is given by…”

Localization of energy for a regular black hole solution in an asymptotically de Sitter spacetime geometry

“…The localization of energy for non-singular black hole solutions by using different energy-momentum complexes has been activated rather recently, when interesting studies [60][61][62][63] arose. In particular, the energy of the Ayón-Beato-García black hole solution has been computed in [64,65] by using the Einstein, Weinberg and Møller prescriptions, while in our paper we study the energy and momentum distribution of the Ayón-Beato-García-Bronnikov-de Sitter (ABGB-dS) regular black hole in an asymptotically de Sitter spacetime geometry [66]. Our calculations have been performed by applying the Einstein, Landau-Lifshitz, Weinberg and Møller prescriptions and using Mathematica and Maple, the last having attached the GrTensor platform.…”