Nonlinear Electrodynamics Theory Research Articles

Exact black holes in string-inspired Euler-Heisenberg theory

We consider higher-order derivative gauge field corrections that arise in the fundamental context of dimensional reduction of string theory and Lovelock-inspired gravities and obtain an exact and asymptotically flat black hole solution, in the presence of nontrivial dilaton configurations. Specifically, by considering the gravitational theory of Euler-Heisenberg nonlinear electrodynamics coupled to a dilaton field with specific coupling functions, we perform an extensive analysis of the characteristics of the black hole, including its geodesics for massive particles, the energy conditions, thermodynamical and stability analysis. The inclusion of a dilaton scalar potential in the action can also give rise to asymptotically (anti) de Sitter spacetimes and an effective cosmological constant. Moreover, we find that the black hole can be thermodynamically favored when compared to the Gibbons-Maeda-Garfinkle-Horowitz-Strominger black hole for those parameters of the model that lead to a larger black hole horizon for the same mass. Finally, it is observed that the energy conditions of the obtained black hole are indeed satisfied, further validating the robustness of the solution within the theoretical framework, but also implying that this self-gravitating dilaton-nonlinear-electrodynamics system constitutes another explicit example of bypassing modern versions of the no-hair theorem without any violation of the energy conditions. Published by the American Physical Society 2024

Born again

Born’s original 1933 theory of nonlinear electrodynamics (in contrast to the later Born-Infeld theory) is acausal for strong fields. We explore the issue of strong-field causality violation in families of theories containing Born and/or Born-Infeld, and many variants that have been previously proposed in contexts that include cosmology and black hole physics. Many of these variants are acausal and hence unphysical. A notable exception is the modified Born-Infeld theory with ModMax as its conformal weak-field limit.

Nonlinearly charged black holes: Shadow and thin-accretion disk

In this paper, we explore the effect of the parameters of non-linear electrodynamics (NLED) and magnetic charges on various aspects of black holes (BH) arising in the particular NLED theory. More precisely, we look into the behavior of photons around the BH and produce shadow by considering a thin accretion disk model. We initially examine the overall behavior of the photon sphere and the corresponding shadow silhouette under the effects of these parameters. Using the EHT data for Sgr. A* and M87*, we provide constraints on the magnetic charge qm. Our results indicate that M87* gives better constraints, and as the value of the NLED coupling parameter β is increased, the constrained range for qm widens. At lower values of qm, we find that the shadow radius is close to the observed value. Then, we study different other aspects, such as the energy emitted by the accretion disk, the temperature of the disk around the BH, and the nature of light it gives off. We also look at how the black hole shadow appears in different situations. Finally, we investigate how the magnetic charge affects all the above mentioned aspects when we take into account NLED along with gravity. This study helps us understand the complex relationship between magnetic charge and its effect on various aspects related to a BH.

Light propagation in the vicinity of the ModMax black hole

ModMax is a nonlinear electrodynamics theory with the same symmetries as Maxwell electrodynamics. Static spherically symmetric solutions have been derived by coupling ModMax electrodynamics with the Einstein equations, which can represent a black hole. In this paper, we analyze light propagation in the vicinity of the ModMax black hole. We determine birefringence, light trajectories, deflection, redshifts, as well as the shadow of the black hole using the effective or optical metric to determine the optical paths of light; comparison is done with the corresponding effects in the neighborhood of the Reissner-Nordstrom black hole, that is the solution to the Einstein-Maxwell equations.

Exact multicentered static point charge source distributions in the Born–Infeld theory of nonlinear electromagnetism and presence of electric and magnetic currents

Exact multicentered solutions to the governing equations of the Born–Infeld nonlinear theory of electrodynamics describing distributions of electric, magnetic, and dyonic point charge sources are constructed explicitly for the first time. The method of construction may effectively be adapted to obtain such solutions in generalized theories as well. As a consequence, the solutions unveil that, in order to achieve a balance between such multicentered electric or magnetic point charge distribution in equilibrium, a static magnetic or electric current must be present, resulting in non-conservativeness of the induced electric or magnetic intensity field, respectively and universally. Moreover, it is also shown that the methods of construction and conclusions drawn in the multicentered situation may be extended to obtain exact solutions and similar conclusions, explicitly, in the situation of continuously distributed charge source problems.

Solutions and basic properties of regularized Maxwell theory

The regularized Maxwell theory is a recently discovered theory of nonlinear electrodynamics that admits many important gravitating solutions within the Einstein theory. Namely, it was originally derived as the unique nonlinear electrodynamics (that depends only on the field invariant ${F}_{\ensuremath{\mu}\ensuremath{\nu}}{F}^{\ensuremath{\mu}\ensuremath{\nu}}$) whose radiative solutions can be found in the Robinson-Trautman class. At the same time, it is the only electrodynamics of this type (apart from Maxwell) whose slowly rotating solutions are fully characterized by the electrostatic potential. In this paper, after discussing the basic properties of the regularized Maxwell theory, we concentrate on its spherical electric solutions. These not only provide ``the simplest'' regularization of point electric field and its self-energy, but also feature complex thermodynamic behavior (in both canonical and grand canonical ensembles) and admit an unprecedented phase diagram with multiple first-order, second-order, and zeroth-order phase transitions. Among other notable solutions, we construct a novel C-metric describing accelerated AdS black holes in the regularized Maxwell theory. We also present a generalization of the regularized Maxwell Lagrangian applicable to magnetic solutions, and find the corresponding spherical, slowly rotating, and weakly Newman-Unti-Tamburino charged solutions.

Solutions in Nonlinear Electrodynamics and their double copy regular black holes

We study solutions in non-linear electrodynamics (NED) and establish several general results. We show, that the SO(2) electric-magnetic duality symmetry is restrictive enough to allow for reconstruction of the NED Lagrangian from the spherically-symmetric electrostatic (Coulomb-like) solution — although there are infinitely many different NED theories admitting a given solution, there exists a unique SO(2) invariant one among them under a simple analyticity assumption (that leaves out some interesting physical theories). We introduce a general algorithm for constructing new SO(2) invariant NED theories in the conventional approach, where only a few examples are available. We also show how to derive the Lagrangian of the SO(2) invariant theory admitting a given electrostatic solution. We further show on a simple example that some NED theories may require sources (particles) of finite (non-zero) size. Such a non-zero size source not only regularizes the infinite energy of the point charge but also satisfies the condition of regularity, that the electric field is zero at the origin. The latter condition was identified earlier as necessary and sufficient for the NED solution to generate a regular black hole via so-called double copy construction and is also satisfied by solitons. We propose a large class of solitonic NED solutions that give rise to regular black holes via double copy construction and contain solutions of Maxwell and Born-Infeld as different limits. This class of NED solutions acquires two new properties in the limit where the corresponding regular black hole’s asymptotics becomes Minkowski: it gives rise to regular higher-spin black holes via generalization of double copy — “higher-copy” construction, and for very short distances changes the sign of the force becoming repulsive/attractive for opposite/similar signs of charges.

Tidal forces in dirty black hole spacetimes

Black holes can be inserted in very rich astrophysical environments, such as accretion disks. Although isolated black holes are simple objects in general relativity, their accretion disks may significantly enrich the field configurations of their surroundings. Alternative theories of gravity can lead to novel black hole solutions, which can be represented by small deviations in the metric due to an effective stress-energy tensor. Among the key aspects of the interaction of black holes with their surroundings, stand tidal forces phenomena. We study the tidal forces of spherically symmetric black holes in the presence of effective matter fields, dubbed as dirty black holes. These effective fields can generically represent usual or exotic matter associated to a variety of gravity theories. We show that this dirtiness leads to characteristic imprints in the tidal forces, which are absent in the case of a black hole surrounded by vacuum. We apply our results to particular cases, such as black holes coupled to linear and nonlinear electrodynamics theories and a Schwarzschild black hole surrounded by a spherical shell.

AdS–dS stationary rotating black hole exact solution within Einstein-nonlinear electrodynamics

In this report the exact rotating charged black hole solution to the Einstein–nonlinear electrodynamics theory with a cosmological constant is presented. This black hole is equipped with mass, rotation parameter, electric and magnetic charges, cosmological constant Λ, and three parameters due to the nonlinear electrodynamics: β is associated to the potential vectors Aμ and ⋆Pμ, and two constants, F0 and G0, due to the presence of the invariants F and G in the Lagrangian L(F(xμ),G(xμ)). This solution is of Petrov type D, characterized by the Weyl tensor eigenvalue Ψ2, the traceless Ricci tensor eigenvalue S=2Φ(11), and the scalar curvature R; it allows for event horizons, exhibits a ring singularity and fulfils the energy conditions. Its Maxwell limit is the de Sitter-Anti–de Sitter–Kerr–Newman black hole solution.

ModMax meets Susy

We give a prescription for mathcal{N} = 1 supersymmetrization of any (four-dimensional) nonlinear electrodynamics theory with a Lagrangian density satisfying a convexity condition that we relate to semi-classical unitarity. We apply it to the one-parameter ModMax extension of Maxwell electrodynamics that preserves both electromagnetic duality and conformal invariance, and its Born-Infeld-like generalization, proving that duality invariance is preserved. We also establish superconformal invariance of the superModMax theory by showing that its coupling to supergravity is super-Weyl invariant. The higher-derivative photino-field interactions that appear in any supersymmetric nonlinear electrodynamics theory are removed by an invertible nonlinear superfield redefinition.

Deformed hopfion-Rañada knots in ModMax electrodynamics

Source-free so-called ModMax theories of nonLinear electrodynamics (NLE) in the four dimensional Minkowski spacetime vacuum are the only possible continuous deformations—and as a function of a single real and positive parameter—of source-free Maxwell linear electrodynamics (MLE) in the same vacuum, which preserve all the same Poincaré and conformal spacetime symmetries as well as the continuous duality invariance of Maxwell’s theory. Null field configurations of the latter however, including null electromagnetic knots, are singular for the Lagrangian formulation of any spacetime Poincaré and conformal invariant theory of NLE. In particular null hopfion-Rañada (HR) knots are a distinguished and fascinating class on their own of topologically nontrivial solutions to Maxwell’s equations. This work addresses the fate of these configurations within ModMax theories. A doubled class of ModMax deformed HR knots is thereby identified, each of which coalescing back in a continuous fashion to the original HR knot when the nonlinear deformation parameter is turned off.

Thermodynamics and heat engines of black holes with Born–Infeld-type electrodynamics

In this paper, we have studied electrically charged black holes in a new model of nonlinear electrodynamics introduced by Kruglov in Mod. Phys. Lett. A 32, 1750201 (2017). 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 we have discussed how the parameters in the nonlinear electrodynamics theory affect the efficiency of the heat engine.

Taub-NUT solutions in conformal electrodynamics

We construct a novel charged Taub-NUT spacetime, providing a first non-trivial example of a self-gravitating solution to the recently proposed ModMax theory [1,2], the most general (1-parametric) theory of non-linear electrodynamics that is characterized by both the conformal symmetry and the SO(2) duality-rotation invariance. The spacetime features non-trivial magnetic fields, in their presence the non-linearity of the field becomes apparent and the solution is distinguished from that of the Maxwell theory. The thermodynamics of the new solution, the charged black hole limit of vanishing NUT parameter, and the self-dual solutions are also briefly discussed.

Can the power Maxwell nonlinear electrodynamics theory remove the singularity of electric field of point-like charges at their locations?

We introduce a variable power Maxwell nonlinear electrodynamics theory which can remove the singularity of electric field of point-like charges at their locations. One of the main problems of Maxwell's electromagnetic field theory is related to the existence of singularity for the electric field of point-like charges at their locations. In other words, the electric field of a point-like charge diverges at the charge location which leads to an infinite self-energy. In order to remove this singularity a few nonlinear electrodynamics (NED) theories have been introduced. The Born-Infeld (BI) NED theory is one of the most famous among them. However the power Maxwell (PM) NED cannot remove this singularity. In this paper, we show that the PM NED theory can remove this singularity, when the power of PM NED is less than .

Teleparallel gravity coupled to matter content from nonlinear electrodynamics with dyonic configuration

This paper considers a static, spherically symmetric spacetime in the context of teleparallel equivalent of General Relativity coupled to the matter content from nonlinear electrodynamics (NED) supported by gauge-invariant Lagrangians, seeking the feasibility of achieving nonsingular solutions. In this setup, the well-known NED solutions, i.e., the Bardeen and Hayward black holes (BHs) are first examined. Then, some specific dyonic configurations, involving both radial electric and magnetic fields, in the teleparallel gravity framework are analysed. For the special case of a Born-Infeld NED theory, a generalized dyonic Reissner–Nordstrom (RN) solution is obtained in terms of the radial coordinate which exhibits a singular behavior at the origin. Nonetheless, the appearance of a naked singularity is impossible in the adopted Born-Infeld (BI) spacetime. The location and size of horizons depend on the BI parameter, leading to the concept of a hairy BH. However, at infinity it is not distinguishable from a dyonic RNBH characterized only by global charges such as ADM mass, electric and magnetic charges.

N + 1-Dimensional Bertotti–Robinson solutions in gravity coupled with nonlinear electrodynamics

We consider the pure electric type power-law Lagrangian in nonlinear electrodynamics theory of dimensions n + 1. Conformally flat form of Bertotti–Robinson type spacetimes are obtained in all these dimensions with the specific power , which naturally excludes n = 4. This particular dimension is considered separately which is not of power-law form.

Emergent GUP from modified Hawking radiation in Einstein–NED theory

We present a general procedure for constructing exact black hole (BH) solutions with a magnetic charge in the context of nonlinear electrodynamics (NED) theory as well as in the coherent state approach to noncommutative geometry (NCG). In this framework, the Lagrangian density for a noncommutative Hayward BH is obtained and the weak energy condition is satisfied. The noncommutative Hayward solution depends on two kind of charges, without which the Schwarzschild solution is applicable. Moreover, to find a link between the BH evaporation and uncertainty relations, we may calculate the Hawking temperature and find the effect of the Lagrangian density of BHs on the Hawking radiation. Therefore, a generalized uncertainty principle (GUP) emerges from the modified Hawking temperature in Einstein–NED theory. The origin of this GUP is the combined influence of a nonlinear magnetic source and an intrinsic property of the manifold associated with a fictitious charge. Finally, we find that there is an upper bound on the Lagrangian uncertainty of the BHs that is caused by the NED field and (or) the fictitious charge.

Colliding waves in a model of nonlinear electrodynamics

Bell–Szekeres (BS) solution for colliding electromagnetic waves in Einstein–Maxwell (EM) theory describes also colliding waves in nonlinear electrodynamics (NED) with an emergent cosmological constant. Our NED model covers the first leading orders to the well-known Heisenberg–Euler (HE) type in a particular gauge of pure magnetic field. Prior to the problem of collision we obtain dyonic solution for the considered NED theory in a conformally flat spacetime which has both electric and magnetic fields with constant invariants. Our sole finding is that null currents inevitably arise in the process of collision of plane waves in the HE type NED theory.

A non-abelian analogue of DBI from $T \overline{T}$

The Dirac action describes the physics of the Nambu-Goldstone scalars found on branes. The Born-Infeld action defines a non-linear theory of electrodynamics. The combined Dirac-Born-Infeld (DBI) action describes the leading interactions supported on a single D-brane in string theory. We define a non-abelian analogue of DBI using the T\bar{T}TT‾ deformation in two dimensions. The resulting quantum theory is compatible with maximal supersymmetry and such theories are quite rare.

Magnetically charged black holes from non-linear electrodynamics and the Event Horizon Telescope

Non-linear electrodynamics (NLED) theories are well-motivated extensions of QED in the strong field regime, and have long been studied in the search for regular black hole (BH) solutions. We consider two well-studied and well-motivated NLED models coupled to General Relativity: the Euler-Heisenberg model and the Bronnikov model. After carefully accounting for the effective geometry induced by the NLED corrections, we determine the shadows of BHs within these two models. We then compare these to the shadow of the supermassive BH M87* recently imaged by the Event Horizon Telescope collaboration. In doing so, we are able to extract upper limits on the black hole magnetic charge, thus providing novel constraints on fundamental physics from this new extraordinary probe.