Dyonic and magnetic black holes with nonlinear arcsin-electrodynamics

Abstract

Dyonic and magnetic black holes solutions with spherically symmetric configurations in general relativity are obtained. Black holes possessing electric and magnetic charges are studied where the source of the gravitational field is electromagnetic fields obeying the arcsinelectrodynamics. We find corrections to Coulomb's law and Reissner− Nordström solutions. The principles of causality and unitarity are investigated. We obtain the Hawking temperature and it was shown that at some event horizons there are second-order phase transitions. of relativistic magnetohydrodynamics [12]. The superconductivity was studied in [13] and thermodynamic properties of the dyonic BH were investigated in [14]. All these show the importance of studying dyonic BHs.In this paper we investigate the dyonic BH in the framework of the nonlinear arcsin-electrodynamics. The nonlinear electrodynamics (NED) can solve the problems of singularities in the origin of particles and the problem of infinite self-energy at the classical level. Born and Infeld (BI) [15] proposed the model of NED that can solve problems of singularities. Heisenberg and Euler have shown that QED due to loop corrections gives NED [16]. Then some NED models were appeared that possess similar properties [17]- [27]. NED's coupled to general relativity (GR) were studied in [28]- [40]. Thermodynamics of the BH and corrections to Reisner−Nordström (RN) solutions were investigated [41]- [48]. Electrically and magnetically charged BHs were studied [49]- [56]. It was demonstrated that phase transitions can occur in the BH. Inflation and current acceleration of the universe also can be explained by NED coupled to GR [57]- [66].The paper is organized as follows. The principles of causality and unitarity of arcsin-electrodynamics are considered in section 2. In section 3 the dyonic solution of the BH is obtained. Corrections to Coulomb's law and RN solutions are found. The curvature singularities are studied and we calculate the Kretschmann scalar. The thermodynamics of the BH is considered in section 4. The Hawking temperature of the BH is obtained. In section 5 we study the magnetically charged BH. We show that at some model parameters there can be naked singularities, extremal BH solutions and BH solutions with two horizons. The Hawking temperature and corrections to RN solution are found. We show the possibility of phase transitions in the BH. Section 6 is devoted to a conclusion.We use units with c = 1, k B = 1, and signature η = diag(−, +, +, +).

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

“…In other words, the model (5.13) does not permit a point electric charge but a monopole. A model that is in close resemblance to the classical Born-Infeld theory [18] and involves an arcsin-type nonlinearity [60,61] is given by…”

“…Then the behavior of A(r) described implies A (r + ) ≥ 0. This property allows us to calculate the Hawking black hole temperature [41,61,74]…”

“…As another example, we consider the dyonic black hole for the arcsin-model [60,61] with Hamiltonian density (7.24). Hence, inserting (7.24) into (10.15), we have which gives us the asymptotic expression…”

“…In fact, such models are known to exist in literature. For example, we will see that in the arcsin-model [60,61] and a subclass of the fractional-powered model [62], monopoles are not allowed, although electric point charges are allowed, in view of the finite-energy condition. Instead of considering individual models, here, we shall show that such a breakdown of electric and magnetic point charge symmetry, referred to as electromagnetic asymmetry, may be regarded as a generic property of nonlinear electrodynamics.…”

Particle motion around generic black holes coupled to non-linear electrodynamics

“…We assume the above assumptions on parameters and black hole solution for the rest of this paper. The energy conditions were tested in [4] or [45][46][47] and even more restrictive causality and unitarity conditions were studied in [48].…”