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

Abstract

We obtain an exact static solution to Einstein-Power-Maxwell (EPM) theory in (2 + 1) dimensional AdS spacetime, in which the scalar field couples to gravity in a non-minimal way. After considering the scalar potential, a stable system leads to a constraint on the power parameter k of Maxwell field. The solution contains a curvature singularity at the origin and is non-conformally flat. The horizon structures are identified, which indicates the physically acceptable lower bound of mass in according to the existence of black hole solutions. Especially for the cases with k > 1, the lower bound is negative, thus there exist scalar black holes with negative mass. The null geodesics in this spacetime are also discussed in detail. They are divided into five models, which are made up of the cases with the following geodesic motions: no-allowed motion, the circular motion, the elliptic motion and the unbounded spiral motion.

ModMax model of nonlinear electrodynamics without the linear term

“…[16,17]. Its applications in the physics of the black holes have been demonstrated through several works [18][19][20][21][22][23][24][25][26][27][28][29].…”

Static-fluid black hole and wormhole in three-dimensions

“…This in turn means that the static-fluid satisfies non of the energy conditions, and therefore it is an exotic fluid. Furthermore, from (21) i.e. f (r) = ρ(r) ρc , with ρ (r) < 0 we have to set ρ c < 0 and consequently the line element becomes…”

“…The most significant one is that there is no vacuum solution in 2+1-dimensions. Hence, one should add sources such as cosmological constant [9,10], electromagnetic (both linear and non-linear) field [11][12][13] and scalar fields to couple with such sources [14][15][16][17][18][19][20][21][22]. In Bañados, Teitelboim & Zanelli (BTZ) black hole solution, it is the cosmological constant that bends the spacetime and forms BTZ black hole.…”

Exact hairy black holes asymptotically $AdS_{2+1}$

“…Indeed in this manifold, the Riemann tensor is a function of the Ricci tensor and metric R αβγσ (R µν , g µν ), them if we consider the Einstein-Hilbert action there is no solutions, nevertheless, when a negative cosmological constant is considered Banados, Teitelboim and Zanelli found the BTZ black hole solution [3,4]. The procedure to overcome the non-hair theorem consist in coupling (minimal, non-minimal or conformal) another fields to Einstein-Hilbert, but under the special conditions [2,[5][6][7][8][9][10], And no less important is the route of higherderivative gravities [11][12][13], another examples with scalar hair and gauge fields in fourth dimensions can be found in [14][15][16][17][18][19][20] Here we present a family of hairy black hole solutions in three dimensions with a non-trivial scalar potential minimally coupling. This scalar field contributes to the metric, therefore, in to the thermodynamics of the black hole.…”