Four-parametric regular black hole solution

Abstract

We present a regular class of exact black hole solutions of the Einstein equations coupled with a nonlinear electrodynamics source. For weak fields the nonlinear electrodynamics becomes the Maxwell theory, and asymptotically the solutions behave as the Reissner-Nordström one. The class is endowed with four parameters, which can be thought of as the mass m, charge q, and a sort of dipole and quadrupole moments α and β, respectively. For α ≥ 3, β ≥ 4, and |q| ≤ 2s c m the corresponding solutions are regular charged black holes. For α = 3, they also satisfy the weak energy condition. For α = β = 0 we recover the Reissner-Nordström singular solution and for α = 3, β = 4 the family includes a previous regular black hole reported by the authors. Keywords Regular black hole · Nonlinear electrodynamicsOne of the active research topics on black hole physics in recent years has been related with its interior behavior. It is clear now that black holes are not necessarily singular and several examples of regular exact black hole solutions has been reported in the literature [1][2][3][4].The research on this subject started with the pioneering work of Bardeen [5] who proposed the first regular black hole model (see also Refs. [4,6,7]). The Bardeen model is a regular black hole satisfying the weak energy condition and it was a crucial guidance on the ulterior investigations related

Rotating charged black hole with Weyl corrections

“…The Bardeen black holes can be interpreted as the solution to a nonlinear magnetic monopole with a mass M and a charge q [21]. The Bardeen black holes are also generalized to the model with four specific parameters [22]. Recently, a large class of black hole solutions have been constructed in the power Maxwell theory [23][24][25][26] in which the Maxwell action takes as power-law function of the form L = −β(F µν F µν ) k , where β is a coupling constant and k is a power parameter.…”

A nonsingular rotating black hole

“…However, the physical source associated to a Bardeen solution was clarified much later by Ayon-Beato and Garcia [12]. The exact self-consistent solutions for the regular black hole for the dynamics of gravity coupled to nonlinear electrodynamics had also been obtained later [13][14][15], which also share most properties of the Bardeen's black hole. Subsequently, there has been intense activity in the investigation of regular black holes as in [4,[16][17][18][19][20], and more recently in [21][22][23][24], but most of these solutions are more or less based on Bardeen's proposal.…”

Nonlinearly charged Lifshitz black holes for any exponent z > 1

“…It is important to emphasize that in many cases both formalisms are not equivalent since as it occurs in standard Legendre transforms, the equivalence depends on the invertibility of the conjugate relations, which for electrodynamics are embodied in the constitutive relations (2.2c). In fact, there are well behaved nonlinear electrodynamics where the Lagrangian cannot be written as a single function of the invariants of F µν ; relevant examples are those giving rise to regular black holes [23][24][25][26][27]. This is also the case we consider here.…”

“…The renewal interest on nonlinear electrodynamics matches with their emergence and importance in the low energy limit of heterotic string theory. Also, nonlinear electrodynamics have been proved to be a powerful and useful tool in order to construct black hole solutions with interesting features and properties as for example regular black holes [23][24][25][26][27] or black holes with nonstandard asymptotic behaviors in Einstein gravity or some of its generalizations [28][29][30][31][32][33][34][35][36][37][38]. Charged black hole solutions emerging from nonlinear theories also have nice thermodynamics properties which make them attractive to be studied.…”