Along the last decades, several regular black hole (BH) solutions, i.e., singularity-free BHs, have been proposed and associated to nonlinear electrodynamics models minimally coupled to general relativity. Within this context, it is of interest to study how those nonlinear-electrodynamic-based regular BHs (RBHs) would interact with their astrophysical environment. We investigate the propagation of a massless test scalar field in the background of an electrically charged RBH solution, obtained by Eloy Ayón-Beato and Alberto García. Using a numerical approach, we compute the absorption cross section of the massless scalar field for arbitrary values of the frequency of the incident wave. We compare the absorption cross sections of the Ayón-Beato and García RBH with the Reissner-Nordström BH, showing that they can be very similar in the whole frequency regime.
The time-like naked singularities of the electrically and magnetically charged black hole solutions obtained in a model of nonlinear electrodynamics proposed by Kruglov is investigated within the framework of quantum mechanics. In view of quantum mechanics, the space-time is quantum regular provided that the time evolution of the test quantum wave packet uniquely propagates on an underlying background. Rigorous calculations have shown that when the singularity is probed with specific quantum wave/particle modes, the quantum wave operator turns out to be essentially self-adjoint. Thus, the time…
We derive the equations for the odd and even parity perturbations of coupled electromagnetic and gravitational fields of a black hole with an electric charge within the context of general nonlinear electrodynamics. The Lagrangian density is a generic function of the Lorentz invariant scalar quantities of the electromagnetic fields. We include the Hodge dual of the electromagnetic field tensor and the cosmological constant in our calculations. For each type of parity, we reduce the system of Einstein field equations coupled to nonlinear electrodynamics to two coupled Schrödinger-type wave equat…
This paper aims to investigate the astrophysical applicability of the electrically and magnetically charged black hole solutions obtained in a model of nonlinear electrodynamics proposed by Kruglov (Ann. Phys. Berlin 2017, 529, 170073). Theoretical calculations of the bending angles and gravitational redshifts from the theory of general relativity are studied numerically by using the stellar data of charged compact objects and a hypothetical quark star model. Calculations have revealed that although the theoretical outcomes differ from the linear Maxwell case, the plotted bending angles coinci…
Nonlinear electrodynamic (NLED) theories are well-motivated for their extensions to classical electrodynamics in the strong field regime, and have been extensively investigated in seeking for regular black hole solutions. In this paper, we focus on two spherically symmetric and static black hole solutions based on two types of NLED models: the Euler-Heisenberg NLED model and the Bronnikov NLED model, and calculate the weak deflection angle of light by these two black holes with the help of the Gauss-Bonnet theorem. We investigate the effects of the one-loop corrections to quantum electrodynami…
We address the question of existence of regular spherically symmetric electrically charged solutions in Nonlinear Electrodynamics coupled to General Relativity. Stress-energy tensor of the electromagnetic field has the algebraic structure $T_0^0=T_1^1$. In this case the Weak Energy Condition leads to the de Sitter asymptotic at approaching a regular center. In de Sitter center of an electrically charged NED structure, electric field, geometry and stress-energy tensor are regular without Maxwell limit which is replaced by de Sitter limit: energy density of a field is maximal and gives an effect…
We present the full set of analytical solutions of the geodesic equations of charged test particles in the Reissner-Nordström space-time in terms of the Weierstraß $\wp$, $σ$ and $ζ$ elliptic functions. Based on the study of the polynomials in the $\vartheta$ and $r$ equations we characterize the motion of test particles and discuss their properties. The motion of charged test particles in the Reissner-Nordström space-time is compared with the motion of neutral test particles in the field of a gravitomagnetic monopole. Electrically or magnetically charged particles in the Reissner-Nordström sp…
The \textit{axial} electromagnetic (EM) perturbations of the black hole (BH) solutions in general relativity coupled to nonlinear electrodynamics (NED) were studied for both electrically and magnetically charged BHs, assuming that the EM perturbations do not alter the spacetime geometry in our preceding paper [Phys. Rev. D 97, 084058 (2018)]. Here, as a continuation of that work, the formalism for the \textit{polar} EM perturbations of the BHs in general relativity coupled to the NED is presented. We show that the quasinormal modes (QNMs) spectra of polar EM perturbations of the electrically a…
In nonlinear electrodynamics coupled to gravity, regular spherically symmetric electrically charged solutions satisfy the weak energy condition and have obligatory de Sitter centre. By the Gürses-Gürsey algorithm they are transformed to spinning electrically charged solutions asymptotically Kerr-Newman for a distant observer. Rotation transforms de Sitter center into de Sitter vacuum surface which contains equatorial disk $r=0$ as a bridge. We present general analysis of the horizons, ergoregions and de Sitter surfaces, as well as the conditions of the existence of regular solutions to the fie…
The characteristic time of disappearance of electric field in massive electrodynamics during the capture of electric charge by black holes is calculated. It is shown that this time does not depend upon the photon mass. The electric field at large distances disappears with the speed of light.
A regular static, spherically symmetric electrically charged black hole solution of general relativity coupled to a new theory for nonlinear electrodynamics is presented. This theory has the interesting feature that, at far distances from the black hole, in the weak field limit, the theory reduces to Maxwell Lagrangian with Heisenberg-Euler correction term of quantum electrodynamics. The singular center of the black hole is replaced by flat, de Sitter, or anti de Sitter space, if the spacetime in which the black hole is embedded is asymptotically flat, de Sitter, or anti de Sitter, respectivel…
We find non-commutative inspired electrically and magnetically charged black hole solutions in Euler-Heisenberg non-linear electrodynamics. For these solutions, we determine the non-commutative corrections to the horizon radius for the general and extremal case. We also analyse the weak, dominant and strong energy conditions and the shadow associated with these metrics.
We study the geodesics of charged black holes in polynomial Maxwell Lagrangians, a subclass of models within the nonlinear electrodynamics (NLED). Specifically, we consider black holes in Kruglov, power-law, and Ayon-Beato-Garcia models. Our exploration on the corresponding null bound states reveals that photon can orbit the extremal black holes in stable radii outside the corresponding horizon. The reason behind this is the well-known theorem that a photon in a NLED background propagates along its own {\it effective} geometry. This nonlinearity is able to shift the local minimum of the effect…
We analyzed the frequency shifts of photons emitted from massive particles that move in stable geodesics around black holes with non-linear electrodynamics. The motion of the photon is modified by an effective metric when the Einstein gravity is coupled with non-linear electrodynamics. The kinematic shifts for photons are modified by the magnetic and electric factors that make the difference between the linear and non-linear electrodynamics. As an illustration, we present the frequency shifts of the photons for black holes with non-linear electrodynamics, two magnetic black holes, and two elec…
The electromagnetic (EM) perturbations of the black hole solutions in general relativity coupled to nonlinear electrodynamics (NED) are studied for both electrically and magnetically charged black holes, assuming that the EM perturbations do not alter the spacetime geometry. It is shown that the effective potentials of the electrically and magnetically charged black holes related to test perturbative NED EM fields are related to the effective metric governing the photon motion, contrary to the effective potential of the linear electrodynamic (Maxwell) field that is related to the spacetime met…
In this paper we present an analysis to determine the existence of singularities in spatially homogeneous anisotropic universes filled with nonlinear electromagnetic radiation. These spaces are conformal to Bianchi spaces admitting a three parameter group of motions G$_3$. For these models we study geodesic completeness. It is shown that with nonlinear electromagnetic field some of the Bianchi spaces are geodesically complete, like G$_3$IX and G$_3$VIII; however, completeness depends on the curvature of the space. When certain topology is assumed, Bianchi G$_3$IX presents geodesics that are im…
It is well known that the Smarr formula does not hold for black holes in non-linear electrodynamics. The main reason for this is the fact that the trace of the energy momentum tensor for nonlinear electrodynamics does not vanish as it is for Maxwell's electrodynamics. Starting from the Komar integral, we derived a new Smarr-type formula for spherically symmetric static electrically charged black hole solutions in nonlinear electrodynamics. We show that this general formula is in agreement with some that are obtained for black hole solutions with nonlinear electrodynamics.
We show that the Bronnikov theorem on the nonexistence of regular electrically charged black holes can be circumvented. In the frame of nonlinear electrodynamics, we present the exact regular black hole solutions of a hybrid type. They are electrically charged, but contain a `dual' core confining a polarization of magnetic charges. The considered example is based on a modification of the Ayón-Beato & Garc\'ıa solution. It represents a very specific realization of the idea on confinement based on dual electrodynamics and dual superconductivity.
Properties of the motion of electrically charged particles in the background of the Gibbons-Maeda-Garfinkle-Horowitz-Strominger (GMGHS) black hole is presented in this paper. Radial and angular motion are studied analytically for different values of the fundamental parameter. Therefore, gravitational Rutherford scattering and Keplerian orbits are analysed in detail. Finally, this paper complements previous work by Fernando for null geodesics (Phys. Rev. D 85: 024033, 2012), Olivares & Villanueva (Eur. Phys. J. C 73: 2659, 2013) and Blaga (Automat. Comp. Appl. Math. 22, 41 (2013); Serb. Astron.…
We present a family of nonlinear electrodynamics models that are free of the infinite self-energy of the point charge. Each model is dependent on a dimensional nonlinearity parameter and is determined by the integer value of a dimensionless parameter n. The Born-Infeld model is recovered when n = 1. Some of the characteristics of this family are studied. In addition, we study the solutions of electrically charged AdS black holes, which result from coupling these electrodynamic models to General Relativity. A Smarr formula consistent with the first law of thermodynamics is also obtained in an e…
We study static, spherically symmetric black holes supported by Euler-Heisenberg theory of electrodynamics and coupled to two different modified theories of gravity. Such theories are the quadratic $f(R)$ model and Eddington-inspired Born-Infeld gravity, both formulated in metric-affine spaces, where metric and affine connection are independent fields. We find exact solutions of the corresponding field equations in both cases, characterized by mass, charge, the Euler-Heisenberg coupling parameter and the modified gravity one. For each such family of solutions, we characterize its horizon struc…
In this paper we have studied electrically charged black holes in a new model of nonlinear electrodynamics introduced by Kruglov in Ref. [1]. There are two parameters for the theory and the black hole could have up to two horizons. Thermodynamics is studied in the extended phase space where the pressure is proportional to the cosmological constant. First law and the Smarr formula are derived. There are phase transitions similar to the Van der Waals liquid-gas phase transitions. Black hole is also studied as a heat engine and have discussed how the parameters in the nonlinear electrodynamics th…
In this article, we construct exact black hole solutions with many horizons (more than number two) in the Einstein-nonlinear electrodynamic theories. In particular, we acquire the explicit expression of nonlinear electrodynamic Lagrangian for the 3-horizon black holes. Then we make the investigations of 3-horizon black holes on the horizons, the null and timelike geodesics, the Love numbers and the thermodynamics.
In this paper, we consider the timelike and null geodesics around the static [GMGHS (Gibbons, Maeda, Garfinkle, Horowitz and Strominger), magnetically charged GMGHS, electrically charged GMGHS] and the rotating (Kerr-Sen dilaton-axion) dilaton black holes. The geodesic equations are solved in terms of Weierstrass elliptic functions. To classify the trajectories around the black holes, we use the analytical solution and effective potential techniques and then characterize the different types of the resulting orbits in terms of the conserved energy and angular momentum. Also, using the obtained …
The electrically charged Born-Infeld black holes in the Palatini formalism for $f(R)$ theories are analyzed. Specifically we study those supported by a theory $f(R)=R\pm R^2/R_P$, where $R_P$ is Planck's curvature. These black holes only differ from their General Relativity counterparts very close to the center, but may give rise to different geometrical structures in terms of inner horizons. The nature and strength of the central singularities are also significantly affected. In particular, for the model $f(R)=R - R^2/R_P$ the singularity is shifted to a finite radius, $r_+$, and the Kretschm…
In this paper we review some properties for the evolving wormhole solution of Einstein equations coupled with nonlinear electrodynamics. We integrate the geodesic equations in the effective geometry obeyed by photons; we check out the weak field limit and find the traversability conditions. Then we analyze the case when the lagrangian depends on two electromagnetic invariants and it turns out that there is not a more general solution within the assumed geometry.
We derive a rotating counterpart of the five-dimensional electrically charged Bardeen regular black holes spacetime by employing the Giampieri algorithm on static one. The associated nonlinear electrodynamics source is computed in order to justify the rotating solution. We thoroughly discuss the energy conditions and the other properties of the rotating spacetime. The black hole thermodynamics of the rotating spacetime is also presented. In particular, the thermodynamic quantities such as the Hawking temperature and the heat capacity are calculated and plotted to see the thermal behavior. The …
It is a well-known fact that light rays do not follow the null geodesics of the space-time in nonlinear electrodynamics; instead, they follow the null geodesics of the so-called effective space-time. Taking this into account, in this paper, we aim to discuss the possibility of distinguishing the type of charge with which the black hole is endowed, via the motion of light rays. The results show that, for any black hole being a charged solution of the field equations of general relativity coupled to the nonlinear electrodynamics, one cannot distinguish the two types of charge (magnetic or electr…
We study the geodesic motion of massless test particles in the background of a magnetic charged black hole spacetime in four dimensions in dilaton-Maxwell gravity. The behaviour of effective potential in view of the different values of black hole parameters is analysed in the equatorial plane. The possible orbits for null geodesics are also discussed in detail in view of the different values of the impact parameter. We have also calculated the frequency shift of photons in this spacetime. The results obtained are then compared with those for the electrically charged stringy black hole spacetim…
We obtain the mass parameter for a class of static and spherically symmetric regular black holes (BHs) (namely Bardeen, Hayward and Ayón-Beato-García BHs) which are solutions of Einstein's field equations coupled to nonlinear electrodynamics (NED) in terms of redshifts and blueshifts of photons emitted by geodesic particles (for instance, stars) orbiting around these BHs. The motion of photons is not governed by null geodesics for these type of spacetime geometries which reflects the direct effects of the electrodynamic nonlinearities in the photon motion; hence, an effective geometry needs to…
We construct regular rotating black hole and no-horizon spacetimes based on the recently introduced spherically symmetric generic regular black hole spacetimes related to electric or magnetic charge under nonlinear electrodynamics coupled to general relativity that for special values of the spacetime parameters reduce to the Bardeen and Hayward spacetimes. We show that the weak and strong energy conditions are violated inside the Cauchy horizons of these generic rotating black holes. We give the boundary between the rotating black hole and no-horizon spacetimes and determine the black hole hor…
A three-parameter toy-model, which describes a non-minimal coupling of gravity field with electromagnetic field of a relativistic two-component electrically neutral plasma, is discussed. Resonance interactions between particles and transversal waves in plasma are shown to take place due to the curvature coupling effect.
In non-supersymmetric covariant quantum gravity theory, for each system of gravity coupled with single field is one-loop divergent. Since adding other fields or other interactions to each system generates more possible counter-Lagrangian terms, there is room for improvement to restore renormalizability. In this paper, we consider Einstein-Maxwell fields coupled with electrically charged scalar which is the simplest model among the systems of gravity coupled with multiple fields having their own interaction. First, we introduce how to calculate the possible one-loop diagrams in Einstein-SQED sy…
We investigate the Plebański class of electrodynamical theories, i.e., theories of nonlinear vacuum electrodynamics that derive from a Lorentz-invariant Lagrangian (or Hamiltonian). In any such theory the light rays are the lightlike geodesics of two optical metrics that depend on the electromagnetic background field. A set of necessary and sufficient conditions is found whose fulfillment secures that the optical metrics are causal in the sense that the light rays are lightlike or timelike with respect to the underlying space-time metric. Thereupon we derive conditions on the Lagrangian, or th…
In this work we extend and generalize our previous work on the scale dependence at the level of the effective action of black holes in the presence of non-linear electrodynamics. In particular, we consider the Einstein-power-Maxwell theory without a cosmological constant in (2+1) dimensions, assuming a scale dependence of both the gravitational and the electromagnetic coupling and we investigate in detail how the scale--dependent scenario affects the horizon and thermodynamic properties of the classical black holes for any value of the power parameter. In addition, we solve the corresponding e…
The expressions for the quasinormal modes (QNMs) of black holes with nonlinear electrodynamics, calculated in the eikonal approximation, are presented. In the eikonal limit QNMs of black holes are determined by the parameters of the circular null geodesics. The unstable circular null orbits are derived from the effective metric that is the one obeyed by light rays under the influence of a nonlinear electromagnetic field. As an illustration we calculate the QNMs of four nonlinear electromagnetic black holes, two singular and two regular, namely from Euler-Heisenberg and Born-Infeld theories, fo…
We study quasinormal modes (QNMs) in 5D electrically charged Bardeen black holes spacetime by considering the scalar and electromagnetic field perturbations. The black holes spacetime is an exact solution of Einstein gravity coupled to nonlinear electrodynamics in five dimensions, which has nonsingular behavior. To calculate QNMs, we use the WKB approximation method up to sixth order. Due to the presence of electric charge $q_e > 0$, both the scalar and electromagnetic field perturbations decay more slowly when compared to the Schwarzschild-Tangherlini black holes. We discover that the scalar …
In this paper, we use previously developed exact solutions to present some of the curious features of a force-free magnetosphere in a Kerr background. More precisely, we obtain a hitherto unseen timelike current in the force-free magnetosphere that does not flow along a geodesic. The electromagnetic field in this case happens to be magnetically dominated. This too is a feature that has entered the literature for the first time. Changing the sign of a single parameter in our solutions generates a spacelike current that creates an electromagnetic field that is electrically dominated.
In this article, we considered the strong field approximation of nonlinear electrodynamics black hole and constructed its rotating counterpart by applying the modified Newman-Janis algorithm. The corresponding metric function in the strong field limit of the static black hole is identified in order to study the radius of photon sphere. However, the metric function for the rotating counterpart in the strong field limit is considered in order to study the horizon radius w.r.t spin parameter. We considered the Hamilton-Jacobi method to derive the geodesic equations for photon and constructed an o…
We obtain static and rotating electrically charged black holes of a Einstein-Maxwell-Dilaton theory of the Brans-Dicke type in (2+1)-dimensions. The theory is specified by three fields, the dilaton, the graviton and the electromagnetic field, and two parameters, the cosmological constant and the Brans-Dicke parameter. It contains eight different cases, of which one distinguishes as special cases, string theory, general relativity and a theory equivalent to four dimensional general relativity with one Killing vector. We find the ADM mass, angular momentum, electric charge and dilaton charge and…
