Holes In Nonlinear Electrodynamics Research Articles

Aschenbach effect and circular orbits in static and spherically symmetric black hole backgrounds

The Aschenbach effect, the increasing behavior of the angular velocity of a timelike circular orbit with its radius coordinate, is found to extensively exist in rapidly spinning black holes to a zero-angular-momentum observer. It also has potential observation in the high-frequency quasi-periodic oscillations of X-ray flux. However, observing such effect remains to be a challenge in static and spherically symmetric black hole backgrounds. In this paper, we mainly focus on such issue. Starting with the geodesics, we analytically study the underlying properties of the timelike circular orbits, and show the conditions under which the Aschenbach effect survives. It is shown that the presence of the static point orbits and stable photon spheres would be the indicator of the Aschenbach effect. We then apply it to three characteristic black holes exhibiting different features. The results state that this effect is absent for both the Schwarzschild and Reissner-Nordström black holes. While, for the dyonic black hole in quasi-topological electromagnetics, there indeed exists the Aschenbach effect. This provides a first example that such effect exists in a non-spinning black hole background. Moreover, it also uncovers an intriguing property for understanding the black holes in nonlinear electrodynamics.

Electrically charged regular black holes in nonlinear electrodynamics: Light rings, shadows, and gravitational lensing

Electrically charged regular black holes in nonlinear electrodynamics: Light rings, shadows, and gravitational lensing

Thermodynamics of BTZ black holes in nonlinear electrodynamics

Thermodynamics of BTZ black holes in nonlinear electrodynamics

Effects of electric and magnetic charges on weak deflection angle and bounding greybody of black holes in nonlinear electrodynamics

In this paper, we study the weak deflection angle using the Gauss–Bonnet theorem and bounding greybody factor for electric and magnetic black holes in the background of nonlinear electrodynamics. Using Gibbons and Werner’s approach, we first acquired the Gaussian optical curvature to be used in the Gauss–Bonnet theorem and calculate the bending angle for spherically symmetric electric and magnetic black holes in both non-plasma and plasma mediums in the weak field limits. Later, we calculate the rigorous bounds of the greybody factor for the given black holes. Furthermore, we are looking into the graphical behaviour of bending angles and greybody bounds at specific values of multiple parameters as well as black hole charges. It is to be mentioned here that all the results for the electric and magnetic-charged black hole solutions are reduced into the Schwarzschild black hole solution in the absence of the black hole charges.

Testing black holes in non-linear electrodynamics from the observed quasi-periodic oscillations

Quasi-periodic oscillations (QPOs), in particular, the ones with high frequencies, often observed in the power spectrum of black holes, are useful in understanding the nature of strong gravity since they are associated with the motion of matter in the vicinity of the black hole horizon. Interestingly, these high frequency QPOs (HFQPOs) are observed in commensurable pairs, the most common ratio being 3:2. Several theoretical models are proposed in the literature which explain the HFQPOs in terms of the orbital and epicyclic frequencies of matter rotating around the central object. Since these frequencies are sensitive to the background spacetime, the observed HFQPOs can potentially extract useful information regarding the nature of the same. In this work, we investigate the role of regular black holes with a Minkowski core, which arise in gravity coupled to non-linear electrodynamics, in explaining the HFQPOs. Regular black holes are particularly interesting as they provide a possible resolution to the singularity problem in general relativity. We compare the model dependent QPO frequencies with the available observations of the quasi-periodic oscillations from black hole sources and perform a χ2 analysis. Our study reveals that most QPO models favor small but non-trivial values of the non-linear electrodynamics charge parameter. In particular, black holes with large values of non-linear electrodynamics charge parameter are generically disfavored by present observations related to QPOs.

Connection between regular black holes in nonlinear electrodynamics and semiclassical dust collapse

There exist a correspondence between black holes in non linear electrodynamics (NLED) and gravitational collapse of homogeneous dust with semi-classical corrections in the strong curvature regime that to our knowledge has not been noticed until now. We discuss the nature of such correspondence and explore what insights may be gained from considering black holes in NLED in the context of semi-classical dust collapse and vice-versa.

Slowly rotating black holes in nonlinear electrodynamics

We show how (at least, in principle) one can construct electrically and magnetically charged slowly rotating black hole solutions coupled to nonlinear electrodynamics (NLE). Our generalized Lense--Thirring ansatz is, apart from the static metric function $f$ and the electrostatic potential $\ensuremath{\phi}$ inherited from the corresponding spherical solution, characterized by two new functions $h$ (in the metric) and $\ensuremath{\omega}$ (in the vector potential) encoding the effect of rotation. In the linear Maxwell case, the rotating solutions are completely characterized by a static solution, featuring $h=(f\ensuremath{-}1)/{r}^{2}$ and $\ensuremath{\omega}=1$. We show that when the first is imposed, the ansatz is inconsistent with any restricted (see below) NLE but the Maxwell electrodynamics. In particular, this implies that the (standard) Newman--Janis algorithm cannot be used to generate rotating solutions for any restricted nontrivial NLE. We present a few explicit examples of slowly rotating solutions in particular models of NLE, as well as briefly discuss the NLE charged Taub-NUT spacetimes.

Dyonic black holes in nonlinear electrodynamics from Kaluza–Klein theory with a Gauss–Bonnet term

Five-dimensional Kaluza–Klein theory with an Einstein–Gauss–Bonnet Lagrangian induces nonlinear corrections to the four-dimensional Maxwell equations, which however remain second-order. Although these corrections do not have effect on the purely electric or magnetic monopole solutions for pointlike charges, they affect the dyonic solutions, smoothing the electric field at the origin for positive values of the Gauss–Bonnet coupling constant. We investigate these solutions in flat space, and then extend them in the presence of a minimal coupling to gravity, obtaining exact charged black hole solutions that generalize the Reissner–Nordström metric.

Weak deflection angle of light in two classes of black holes in nonlinear electrodynamics via Gauss–Bonnet theorem

In this paper, we study the gravitational lensing by some black hole classes within the nonlinear electrodynamics in weak field limits. First, we calculate an optical geometry of the nonlinear electrodynamics black hole and then we use the Gauss–Bonnet theorem for finding deflection angle in weak field limits. The effect of nonlinear electrodynamics on the deflection angle in leading order terms is studied. Furthermore, we discuss the effects of the plasma medium on the weak deflection angle.

Quasinormal modes of charged black holes with corrections from nonlinear electrodynamics

We study quasinormal modes related to gravitational and electromagnetic perturbations of spherically symmetric charged black holes in nonlinear electrodynamics. Beyond the linear Maxwell electrodynamics, we consider a class of Lagrangian with higher-order corrections written by the electromagnetic field strength and its Hodge dual with arbitrary coefficients, and we parametrize the corrections for quasinormal frequencies in terms of the coefficients. It is confirmed that the isospectrality of quasinormal modes under parity is generally violated due to nonlinear electrodynamics. As applications, the corrections for quasinormal frequencies in Euler-Heisenberg and Born-Infeld electrodynamics are calculated, then it is clarified that the nonlinear effects act to lengthen the oscillation period and enhance the damping rate of the quasinormal modes.

Stability of generalized Einstein-Maxwell-scalar black holes

We study the stability of static black holes in generalized Einstein-Maxwell-scalar theories. We derive the master equations for the odd and even parity perturbations. The sufficient and necessary conditions for the stability of black holes under odd-parity perturbations are derived. We show that these conditions are usually not similar to energy conditions even in the simplest case of a minimally coupled scalar field. We obtain the necessary conditions for the stability of even-parity perturbations. We also derived the speed of propagation of the five degrees of freedom and obtained the class of theories for which all degrees of freedom propagate at the speed of light. Finally, we have applied our results to various black holes in nonlinear electrodynamics, scalar-tensor theories and Einstein-Maxwell-dilaton theory. For the latter, we have also calculated the quasinormal modes.

Conformal scalar NUT-like dyons in conformal electrodynamics

We construct conformally scalar NUTty dyon black holes in non-linear electrodynamics (NLE) which possess conformal and duality-rotation symmetries and are characterized by a free dimensionless parameter. The thermodynamic first law of the black hole is formulated. Then we explore the strong gravitational effects of the black hole, mainly focusing on the innermost stable circular orbits (ISCOs) of massive particles and shadows formed by the photons. One of our interesting results is that if the black hole is endowed with a positive real conformal scalar charge rendering it Reissner-Nordstr\"om-like, the radii of the ISCOs and the shadow both increase with the increasing NLE parameter signifying the increasing nonlinearity of the electromagnetic field.

Complexity of black holes in nonlinear electrodynamics

Complexity of black holes in nonlinear electrodynamics

A Smarr formula for charged black holes in nonlinear electrodynamics

It is well known that the Smarr formula does not hold for black holes in nonlinear 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.

Black holes in nonlinear electrodynamics: Quasinormal spectra and parity splitting

We discuss the quasi-normal oscillations of black holes which are sourced by a nonlinear electrodynamic field. While previous studies have focused on the computation of quasi-normal frequencies for the wave or higher spin equation on a fixed background geometry described by such black holes, here we compute for the first time the quasi-normal frequencies for the coupled electromagnetic-gravitational linear perturbations. To this purpose, we consider a parametrized family of Lagrangians for the electromagnetic field which contains the Maxwell Lagrangian as a special case. In the Maxwell case, the unique spherically symmetric black hole solutions are described by the Reissner-Nordstr\"om family and in this case it is well-known that the quasi-normal spectra in the even- and odd-parity sectors are identical to each other. However, when moving away from the Maxwell case, we obtain deformed Reissner-Nordstr\"om black holes, and we show that in this case there is a parity splitting in the quasi-normal mode spectra. A partial explanation for this phenomena is provided by considering the eikonal (high-frequency) limit.

On the thermodynamical stability of black holes in nonlinear electrodynamics

We analyze the thermodynamical stability of static and spherically symmetric black hole solutions with nonlinear electromagnetism as a source, and show that any sequence of such black holes in isolation that includes the Schwarzschild black hole is stable in the (βM,M) plane for any nonlinear Lagrangian describing the electromagnetic field. The study of three exact solutions (which include the Schwarzschild solution in some limit) in the (βQ,Q) plane show that they are stable in the microcanonical ensemble, and unstable or less unstable (due to the existence of a turning point) in the canonical ensemble. If the less unstable configurations are stable, our results indicate that they would be in equilibrium with a reservoir at a higher temperature than the corresponding Reissner–Nordstrom configuration. An expression for the heat capacity at constant charge valid for any Lagrangian describing nonlinear electromagnetism is also presented. It displays a divergence with a change of sign that occurs precisely at the turning point obtained by the Poincarè method.

Quantum statistical relation for black holes in nonlinear electrodynamics coupled to Einstein-Gauss-Bonnet AdS gravity

We consider curvature-squared corrections to Einstein-Hilbert gravity action in the form of Gauss-Bonnet term in D>4 dimensions. In this theory, we study the thermodynamics of charged static black holes with anti-de Sitter (AdS) asymptotics, and whose electric field is described by nonlinear electrodynamics (NED). These objects have received considerable attention in recent literature on gravity/gauge dualities. It is well-known that, within the framework of anti de-Sitter/Conformal Field Theory (AdS/CFT) correspondence, there exists a nonvanishing Casimir contribution to the internal energy of the system, manifested as the vacuum energy for global AdS spacetime in odd dimensions. Because of this reason, we derive a Quantum Statistical Relation directly from the Euclidean action and not from the integration of the First Law of thermodynamics. To this end, we employ a background-independent regularization scheme which consists in the addition to the bulk action of counterterms that depend on both extrinsic and intrinsic curvatures of the boundary (Kounterterm series). This procedure results in a consistent inclusion of the vacuum energy and chemical potential in the thermodynamic description for Einstein-Gauss-Bonnet AdS gravity regardless the explicit form of the NED Lagrangian.

Extremal limit of the regular charged black holes in nonlinear electrodynamics

Solutions of the coupled equations of general relativity and nonlinear electrodynamics with topology ${\mathrm{AdS}}_{2}\ifmmode\times\else\texttimes\fi{}{\mathrm{S}}^{2}$ are constructed and studied both analytically and numerically. It is shown that the near horizon limit of the extreme nonlinear black hole corresponds to the solution expressible in terms of the Lambert special functions. It is explicitly demonstrated that for the formulation of the nonlinear theory considered in this paper the resulting solutions do not belong to the Bertotti-Robinson class unless electrodynamics is Maxwellian. The question of the boundary conditions is briefly discussed.