2+1dimensional magnetically charged solutions in Einstein-power-Maxwell theory

Abstract

We obtain a class of magnetically charged solutions in 2 þ 1 dimensional Einstein-Power-Maxwell theory. In the linear Maxwell limit, such horizonless solutions are known to exist. We show that in 3D geometry, black hole solutions with magnetic charge do not exist even if it is sourced by the powerMaxwell field. Physical properties of the solution with particular power k of the Maxwell field is investigated. The true timelike naked curvature singularity develops when k > 1 which constitutes one of the striking effects of the power-Maxwell field. For specific power parameter k, the occurrence of a timelike naked singularity is analyzed in the quantum mechanical point of view. Quantum test fields obeying the Klein-Gordon and the Dirac equations are used to probe the singularity. It is shown that the class of static pure magnetic spacetime in the power-Maxwell theory is quantum-mechanically singular when it is probed with fields obeying Klein-Gordon and Dirac equations in the generic case.

A new Einstein-nonlinear electrodynamics solution in $$2+1$$ 2 + 1 dimensions

“…In the first paper of Hassaïne and Martínez [9][10][11][12][13][14][15][16][17][18][19][20][21][22] it was shown that the action given in (1) is conformally invariant if k = 3 4 . In this section we set k = 3 4 and = 0 so that the following solution is obtained for the field equations (14)- (16):…”

“…F μν F μν , where, as usual, the field tensor is defined by F μν = ∂ μ A ν − ∂ ν A μ . This Lagrangian belongs to the class of NED with k-power law Maxwell invariant F μν F μν k [9][10][11][12][13][14][15][16][17][18][19][20][21][22]. A similar Lagrangian in 3 + 1 dimensions with magnetic field source has been considered in [23][24][25], and with an electric field as well as both electric and magnetic fields in [26].…”

$$(2+1)$$ ( 2 + 1 ) -Dimensional charged black holes with scalar hair in Einstein–Power–Maxwell Theory

“…Besides sourced by a mass and a negative cosmological constant, pure BTZ black holes can be also to added new sources such as electric/magnetic fields from Maxwell's theory [23][24][25], Maxwell-dilaton [26], rotation [27], perfect fluid [28,29] and others [30,31]. It is interesting to note that the nonlinear electrodynamics (NED) is useful to overcome to eliminate the electromagnetic singularities due to point charges that occur in the linear Maxwell theory.…”

Cloud of strings as source in $$2+1$$ 2 + 1 -dimensional $$f\left( R\right) =R^{n}$$ f

“…The interest started all with the discovery of a 2 + 1-dimensional black hole solution by Banados, Teitelboin and Zanelli (BTZ) [1][2][3][4]. The physical source of the BTZ black hole was a cosmological constant, which was subsequently extended with the presence of different sources [5][6][7][8][9][10][11][12][13][14][15][16][17]. How significant are these sources physically?…”