Shadow of a Nonlinear Electromagnetic Generalized Kerr–Newman–AdS Black Hole

In this study, we present a novel exact solution to the gravitational field equations, known as the Ayón‐Beato–García black hole (BH) solution, set against the backdrop of anti‐de Sitter space and surrounded by a quintessence field (QF). This solution serves as an interpolation between three distinct anti‐de Sitter BH configurations, namely, the Ayón‐Beato–García, Schwarzschild–Kiselev, and the standard Schwarzschild BH solutions. The first aspect of our investigation focuses on the geodesic motion of particles, where we explore how the BH's space‐time geometry‐incorporating the effects of nonlinear electrodynamics (NLED), the QF, and the curvature radius‐influences the dynamics of both massless and massive particles near the BH. To further enrich our analysis, we extend the study to include the perturbative dynamics of a massless scalar field within the BH solution, placing special emphasis on the scalar perturbative potential. Subsequently, we focus into the phenomenon of BH shadows, examining how various parameters, such as the NLED, the curvature of space‐time, and the presence of the QF, impact the size and shape of the shadow cast by the BH. In the final segment of our study, we shift our attention to the thermodynamics of the BH solution. We compute several essential thermodynamic quantities, including the Hawking temperature, specific heat capacity, and Gibbs free energy, analyzing how these properties evolve in response to changes in the various parameters that define the space‐time geometry, which in turn affect the gravitational field when compared to the traditional BH solutions.

Shadow and quasinormal modes of novel charged rotating black hole in Born–Infeld theory: Constraints from EHT results

Based on a regular exact black hole (BH) from nonlinear electrodynamics (NED) coupled to General Relativity, we investigate its stability of such BH through the Quasinormal Modes (QNMs) of electromagnetic (EM) field perturbation and its thermodynamics through Hawking radiation. In perturbation theory, we can deduce the effective potential from nonlinear EM field. The comparison of potential function between regular and RN BHs could predict their similar QNMs. The QNMs frequencies tell us the effect of magnetic charge $q$, overtone $n$, angular momentum number $l$ on the dynamic evolution of NLED EM field. Furthermore we also discuss the cases near extreme condition of such magnetically charged regular BH. The corresponding QNMs spectrum illuminates some special properties in the near-extreme cases. For the thermodynamics, we employ Hamilton-Jacobi method to calculate the near-horizon Hawking temperature of the regular BH and reveal the relationship between classical parameters of black hole and its quantum effect.

Effects of non-linear electrodynamics on thermodynamics of charged black hole

In this paper, we consider black holes in the consistent Aoki-Gorji-Mukohyama theory of the four-dimensional Einstein-Gauss-Bonnet (4D EGB) gravity in the presence of Born-Infeld (BI) nonlinear electrodynamics. We study several optical features of these black holes such as the shadow radius, energy emission rate and deflection angle, and analyse the effect of the coupling constants, the electric charge and cosmological constant on the considered optical quantities. Furthermore, we also employ the connection between the shadow radius and quasinormal modes (QNMs) and investigate small scalar perturbations around the black hole solution. We show that the variation of the parameters of the theory provide specific signatures on the optical features of the BI charged black hole solution, thus leading to the possibility of directly testing this consistent Aoki-Gorji-Mukohyama 4D EGB black hole model by using astrophysical observations.

The theory of nonlinear electrodynamics has got a lot of attentions in recent years. It was shown that Born-Infeld nonlinear electrodynamics is not the only modification of the linear Maxwell's field which keeps the electric field of a charged point particle finite at the origin, and other type of nonlinear Lagrangian such as exponential and logarithmic nonlinear electrodynamics can play the same role. In this paper, we generalize the study on the exponential nonlinear electrodynamics by adding a scalar dilaton field to the action. By suitably choosing the coupling of the matter field to the dilaton field, we vary the action and obtain the corresponding field equations. Then, by making a proper ansatz, we construct a new class of charged dilaton black hole solutions coupled to the exponential nonlinear electrodynamics field in the presence of two Liouville-type potentials for the dilaton field. Due to the presence of the dilaton field, the asymptotic behavior of these solutions are neither flat nor (A)dS. In the limiting case where the nonlinear parameter $\beta^2$ goes to infinity, our solution reduces to the Einstein-Maxwell dilaton black holes. We obtain the mass, temperature, entropy and electric potential of these solutions. We also study the behaviour of the electric field as well as the electric potential of these black holes near the origin. We find that the electric field has a finite value \textit{near} the origin, which is the same as the electric field of Born-Infeld nonlinear electrodynamics, but it can diverge exactly at $r=0$ depending on the model parameters. We also investigate the effects of the dilaton field on the behaviour of the electric field and electric potential. Finally, we check the validity of the first law of black hole thermodynamics on the black hole horizon.

In this paper, we investigate the effect of higher curvature corrections from Gauss–Bonnet gravity on the shadow of charged black holes in both AdS and Minkowski spacetimes. The null geodesic equations are computed in d=5 spacetime dimensions by using the directions of symmetries and Hamilton–Jacobi equation. With the null geodesics in hand, we then proceed to evaluate the celestial coordinates (alpha , beta ) and the radius R_s of the black hole shadow and represent it graphically. The effects of charge Q of the black hole and the Gauss–Bonnet parameter gamma on the radius of the shadow R_s is studied in detail. It is observed that the Gauss–Bonnet parameter gamma affects the radius of the black hole shadow R_s differently for the AdS black hole spacetime in comparison to the black hole spacetime which is asymptotically flat. In particular the radius of the black hole shadow increases with increase in the Gauss–Bonnet parameter in case of the AdS black hole spacetime and decreases in case of the asymptotically flat black hole spacetime. We then introduce a plasma background in order to observe the change in the silhouette of the black hole shadow due to a change in the refractive index of the plasma medium. Finally, we study the effect of the Gauss–Bonnet parameter gamma on the energy emission rate of the black hole which depends on the black hole shadow radius and represent the results graphically.

In this paper, we study gravitational lensing in the weak field limits and the shadow by charged black holes in non-linear electrodynamics corrections. To find the deflection angle in vacuum (non-plasma) up to the leading order terms, we compute the optical Gaussian curvature from optical metric and utilize the Gauss–Bonnet theorem by applying Gibbons and Werner’s technique. Also, we derive the bending angle in plasma and dark matter mediums and observe that the bending angle increases by increasing the effects of these mediums. Further, in vacuum and plasma mediums, we investigate the graphical behavior of the bending angle with respect to the impact parameter u and notice that the bending angle exponentially decreases. Moreover, we calculate the Hawking temperature using the Gauss–Bonnet theorem and compare it with a standard method of computing the Hawking temperature. Furthermore, we investigate the bound of the greybody factor and graphically examine that bound converges to the 1. We relate our obtained results with the results of black holes given in the literature. Finally, we have considered exploring the effect of non-linear electrodynamics (NLED), plasma and dark matter on the black hole’s shadow radius to broaden the study’s scope. Results for the shadow indicate that the three parameters give different deviations to the shadow radius. Interestingly, while plasma affects both the photonsphere and shadow, dark matter only influences the shadow.

Quasinormal modes, shadow and thermodynamics of black holes coupled with nonlinear electrodynamics and cloud of strings

We have studied in this paper the Joule-Thomson expansion of a new charged AdS black hole with a nonlinear electrodynamics in framework of Einstein-Gauss-Bonnet gravity in AdS space. We investigated effects of mass (m), electric charge (q), GB coupling constant (α) and nonlinear electrodynamics parameter (k) on Joule-Thomson expansion by depicting different graphs. The fact that inversion temperature tends to decrease by increasing k, is in contrast to the effect of electric charge. The divergent point as well as the zero point of Joule-Thomson coefficient are also discussed. Results show that, this black hole exhibits a phase transition similar to that of van der Waals system. Furthermore, the isonthalpic curve is obtained and an interesting dependence of these curves on charge and nonlinear electrodynamics parameter is revealed. In T−P graphs, the cooling region shrinks with charge, while this region expands both with mass and with nonlinear electrodynamics parameter. Our study shows that nonlinear electrodynamics parameter plays an important role in Joule Thomson expansion.

We investigate a static and spherically symmetric black hole solution of Einstein gravity sourced by a nonlinear electromagnetic field in the presence of a phantom global monopole. The monopole induces a constant solid-angle deficit, rendering the spacetime asymptotically non-flat, while the nonlinear electromagnetic sector introduces subleading corrections that become relevant in the strong-field regime. The thermodynamics is analyzed using Barrow entropy, which modifies the standard area law through a single deformation parameter. We derive the corresponding internal energy, Helmholtz free energy, and heat capacity, and show that the Barrow deformation parameter significantly affects the phase structure and stability properties, particularly for small horizon radii. The dynamical response of the spacetime is further analyzed through massless Dirac field perturbations. The effective fermionic potential exhibits a single-barrier structure outside the event horizon, allowing for a reliable WKB treatment of the quasinormal modes. The resulting spectra indicate that the imaginary parts of the frequencies remain negative throughout the parameter space considered, confirming linear stability against fermionic perturbations. To further quantify the damping properties of the fermionic ringdown, we analyze the quality factor of Dirac quasinormal modes, which provides a compact measure of the balance between oscillation frequency and decay rate and highlights the influence of the nonlinear electromagnetic sector on the persistence of fermionic perturbations. In addition, we study gravitational lensing using the Gauss–Bonnet theorem, providing a global description of light deflection in both vacuum and plasma environments. The combined effects of nonlinear electrodynamics, the phantom monopole, and plasma dispersion lead to measurable deviations from the Schwarzschild case in the small impact-parameter regime, while the weak-field limit is recovered at large distances.

It is well known that when vacuum polarization emerges in quantum electrodynamics, the non-linear interaction between electromagnetic fields should be considered. Moreover, the corresponding field of non-linear electrodynamics can have important effects on black hole physics. In this work, we focus on the relationship between an observable quantity, that is, the shadow radius, and the first-order phase transition of non-linear charged AdS black holes in the framework of Einstein-power-Yang-Mills gravity. The results show that, under a certain condition, there exists a first-order phase transition from the viewpoint of both the shadow radius and horizon radius, which depend on temperature (or pressure). From the viewpoint of the shadow radius, the phase transition temperature is higher than that from the viewpoint of the horizon radius under the same condition. This may be due to the non-linear Yang Mills charge and the gravitational effect. This indicates that the shadow radius can be regarded as a probe to reveal the thermodynamic phase transition information of black holes. The thermal profiles of coexistent large and small black hole phases when the system is undergoing the phase transition are presented for two different values of the non-linear Yang Mills charge parameter: . Furthermore, the effects of the non-linear Yang Mills charge parameter on the shadow radius and thermal profile are investigated.

In this paper, we investigate the gravitational lensing properties of magnetically charged black holes within the framework of nonlinear electrodynamics. We derive the deflection angle and examine the influence of the nonlinear electrodynamics parameter ξ on light bending. We initially employ a geometric approach based on the Gauss–Bonnet theorem to analyze the gravitational deflection of null and timelike particles. This method encapsulates the global characteristics of the lensing effect in an elegant manner. In the subsequent part of the work, we explore the impact of nonlinear electromagnetic corrections on the black hole shadow. Using numerical techniques, we study the behavior of the photon sphere and demonstrate that a reduction in the photon sphere radius leads to a correspondingly smaller shadow. We compare these results with those for the Schwarzschild and Reissner–Nordström black holes, highlighting the distinctive features introduced by nonlinear electrodynamics. Furthermore, we examine the strong deflection limit for light trajectories near these black holes, focusing on the roles of both the magnetic charge Q and the nonlinear parameter ξ. Our analysis reveals that the combined effects of Q and ξ enhance the strong deflection angle, resulting in a more pronounced lensing effect than that predicted by the classical Reissner–Nordström solution. These findings suggest that the nonlinear interactions may provide a potential observational signature for identifying NED black holes.

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 metric. Consequently, corresponding quasinormal (QN) frequencies differ as well. As a special case, we study new family of the NED black hole solutions which tend in the weak field limit to the Maxwell field, giving the Reissner-Nordstr\"{o}m (RN) black hole solution. We compare the NED Maxwellian black hole QN spectra with the RN black hole QN spectra.

In this work, the charged black hole solution to the Brans-Dicke gravity theory in the presence of the nonlinear electrodynamics has been investigated. To simplify the field equations, a suitable conformal transformation has been used which transforms the Brans-Dicke-Born-Infeld Lagrangian to that of Einstein-dilaton theory with new nonlinear electrodynamics field. A new class of 4-dimensional black hole solution has been constructed out as the exact solution to the Brans-Dicke theory in the presence of the Born-Infeld nonlinear electrodynamics. The physical properties of the solutions have been studied. The black hole charge and temperature have been calculated making use of the Gauss’s law and the concept of surface gravity, respectively. Also, the black hole mass and entropy have been obtained from geometrical methods. Through a Smarr-type mass formula as a function of the black hole charge and entropy the black hole temperature and electric potential, as the intensive parameters conjugate to the black hole entropy and charge, have been calculated.