Electromagnetic Asymmetry, Relegation of Curvature Singularities of Charged Black Holes, and Cosmological Equations of State in View of the Born--Infeld Theory

Abstract

It is shown that, in a generic sense, and unlike what for electric point charges, the Born-Infeld nonlinear electrodynamics excludes monopoles as finite-energy magnetic point charges, thus spelling out an electromagnetic asymmetry. Moreover, it is demonstrated, in a systematic way, that the curvature singularities of finite-energy charged black holes in the context of the Born-Infeld theory may effectively be relegated or in some cases removed under a critical massenergy condition, which has been employed successfully in earlier concrete studies. Furthermore, it is illustrated through numerous examples considered here that, when adapted to describe scalar-wave matters known as k-essences, the Born-Infeld formalism provides a fertile ground for cosmological applications, including achieving accelerated dark-energy expansions and acquiring adequate field-theoretical realizations of the equations of state of various cosmic fluid models.

Dyonically Charged Black Holes Arising in Generalized Born--Infeld Theory of Electromagnetism

“…In Section 5, we use the explicit dyon particle constructions worked out in Section 3 to obtain the exact dyonically charge black hole solutions of the Einstein equations coupled with the classical Born-Infeld model and the exponential model. In the latter situation and under the critical mass-energy condition, we show that the solution becomes regular only when the dyonic charge degenerates itself into a magnetic one as found in [16]. In Section 6, we examine various energy conditions for the examples of the dyonically charged black holes obtained.…”

“…where and in the sequel we choose β > 0 to be a coupling parameter independent of the parameter κ for greater generality such that the limiting situation β = κ 2 returns the model to the classical theory (2.16) and reduces the computation considerably sometimes. The advantage of such a formalism is that (2.17) allows the return to the generalized model [16]…”

“…See [15] for a review on this and other related topics centered around the research on the Born-Infeld theory suggested modified formalism of black hole constructions and cosmological applications. In a recent work [16], the author carried out a systematic study on the relegation of the curvature singularity by the generalized Born-Infeld electrodynamics and established the general conclusion that a finite electromagnetic energy indeed boosts the curvature regularity to the same level of that of the Schwarzschild black hole, K ∼ r −6 , and that when the gravitational mass M equals to the electromagnetic energy, E, a condition referred to as the critical mass-energy condition, the curvature regularity may further be boosted. For example, for the rational-function model of Kruglov [17][18][19], Ma [20] obtained regular magnetically charged black hole solutions, although their electrically charged counterparts are shown [16] to only enjoy a relegated curvature singularity, with K ∼ r −4 .…”

“…In a recent work [16], the author carried out a systematic study on the relegation of the curvature singularity by the generalized Born-Infeld electrodynamics and established the general conclusion that a finite electromagnetic energy indeed boosts the curvature regularity to the same level of that of the Schwarzschild black hole, K ∼ r −6 , and that when the gravitational mass M equals to the electromagnetic energy, E, a condition referred to as the critical mass-energy condition, the curvature regularity may further be boosted. For example, for the rational-function model of Kruglov [17][18][19], Ma [20] obtained regular magnetically charged black hole solutions, although their electrically charged counterparts are shown [16] to only enjoy a relegated curvature singularity, with K ∼ r −4 . In fact, such a feature is already well observed in the Bardeen black hole [8][9][10][11] and the Hayward black hole [12][13][14] situations where the regular solutions are magnetically charged but electrically charged ones are excluded, or vice versa, in view of a correspondence relation called the F -P duality, as a result of the electromagnetic asymmetry of the theory exhibited via the Minkowski spacetime signature.…”

“…As a consequence, Demianski [23] and Gibbons and Rasheed [24] obtained finite-energy dyonically charged black holes in such a context. Inspired by the work of constructing regular magnetically charged black holes [8][9][10][11][12][13][14][15]20] and charged black holes with relegated curvature singularities [16] based on the generalized Born-Infeld nonlinear electrodynamics, the goal of this study is to obtain finite-energy dyonically charged black hole solutions to the Einstein equations coupled with the generalized Born-Infeld electromagnetism based on the invariance principle consideration [6,7]. We shall see that, unlike the Reissner-Nordström charged black hole solution (1.1), these solutions all enjoy relegated curvature singularities with the same order as that of the Schwarzschild black hole at the center of the sources as a consequence of their finite electromagnetic energies and all approach the Reissner-Nordström charged black hole solution (1.1) asymptotically near spatial infinity.…”