Born-Infeld Theory Research Articles

Kerr black hole mimickers sourced by a string fluid

We present rotating solutions of Einstein's gravity coupled to an effective Born-Infeld theory that describes the end of open-string tachyon condensation after the decay of an unstable D-brane or a brane-antibrane system. The geometry of these solutions is that of the rotating frozen star. The solutions are stationary, ultracompact, can be made non-singular via a regularization procedure and their exterior geometry is identical, for all practical purposes, to that of the Kerr solution. The Born-Infeld matter consists of radial electric-flux tubes that emanate from, or end at, the ellipsoidal core of the star. Each end of the flux tubes carries an electric charge, so that the electric field can be viewed as being sourced by an ellipsoidal charge distribution of positive and negative charges near the center of the star. Meanwhile, the star's outer layer is equal and oppositely charged, resulting in a vanishing electric field in the external spacetime. We show that these rotating solutions are ultrastable against radial perturbations, just like their static frozen star counterparts. They are also effectively immune to ergoregion instabilities, as we discuss.

Deflection of light by a compact object with electric charge and magnetic dipole in Einstein–Born–Infeld gravity

We consider the bending of light around a compact astrophysical object with both the electric field and the magnetic field in Einstein–Born–Infeld theory. From the null geodesic of a light ray passing a massive object with electric charge and magnetic dipole, the effective metric was obtained from the light cone condition reflecting the nonlinear electromagnetic effects. We found the asymptotic form of the effective metric up to the first order in gravitational constant G and Born–Infeld parameter 1/β2\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$1/\\beta ^2$$\\end{document} on the equatorial plane. Then we compute the bending angle of light from the geodesic equation. The result includes particular cases where only one type of field is present taking the appropriate limits.

Legendre Transformation in the Born–Infeld Model, Monge–Ampere Equation and Exact Solutions

Legendre Transformation in the Born–Infeld Model, Monge–Ampere Equation and Exact Solutions

Existence of nontrivial solutions for fractional Klein–Gordon equation coupled with Born–Infeld theory with critical exponents

In this paper, we investigate the existence of solutions for a fractional Klein–Gordon equation coupled with Born–Infeld theory when the nonlinearity exhibits critical growth. By overcoming the lack of compactness, we obtain that there is a radially symmetric solution by using variational methods.

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

This work investigates the shadow and quasinormal modes of a novel rotating Born–Infeld-type black hole. First, we study the effect of interaction between nonlinear electrodynamic fields and photons on shadow radius and show that it is less than the error of shadow measurements in Event Horizon Telescope (EHT) observations. Then, we obtain a rotating metric using the Newman–Janis algorithm, starting with the initial metric of the nonrotating novel Born–Infeld black hole solution. Next, we analyze the null geodesics to determine the celestial coordinates. The black hole’s shadow radius is determined by using celestial coordinates. The mass, spin, charge, and nonlinearity parameters all influence the shape and size of the black hole shadow. An increase in the spin parameter results in a gradual reduction in the size of black hole shadows and further distortion of the shadows. Furthermore, constraints on the spin and electric charge of black holes, as well as the nonlinearity parameter, are derived through the utilization of the shadow sizes of supermassive black holes Sagittarius (Sgr) A* and M87* obtained from observations of the EHT. Also, we investigate the correlation between the standard shadow radius and the equatorial and polar quasinormal modes for revolving black holes. Finally, we analyze the emission energy rate from the black hole based on different spacetime parameters. Our observation indicates that the emission energy rate decreases as the values of spin and nonlinearity parameters increase, keeping the charge-to-mass ratios of the Born–Infeld black hole constant.

Pions from higher-dimensional gluons: general realizations and stringy models

In this paper we revisit the general phenomenon that scattering amplitudes of pions can be obtained from “dimensional reduction” of gluons in higher dimensions in a more general context. We show that such “dimensional reduction” operations universally turn gluons into pions regardless of details of interactions: under such operations any amplitude that is gauge invariant and contains only local simple poles becomes one that satisfies Adler zero in the soft limit. As two such examples, we show that starting from gluon amplitudes in both superstring and bosonic string theories, the operations produce “stringy” completion of pion scattering amplitudes to all orders in α′, with leading order given by non-linear sigma model amplitudes. Via Kawai-Lewellen-Tye relations, they give closed-stringy completion for Born-Infeld theory and the special Galileon theory, which are directly related to gravity amplitudes in closed-string theories. We also discuss how they naturally produce stringy models for mixed amplitudes of pions and colored scalars.

Massive covariant colour-kinematics in 3D

We explore topologically massive gauge theories using the covariant colour kinematics duality recently introduced in [1]. We show that the massive bi-adjoint scalar field is simply related to topologically massive gauge theory by the duality, and that enacting the same duality on the gauge theory produces topologically massive gravity coupled to a scalar or, equivalently, an antisymmetric field. We also show that different choices for the replacement of the colour structure constants with kinematic structure constants lead to different theories, including a topologically massive generalisation of Born-Infeld theory.

On the radiation field of a linearly accelerated charged particle in Born–Infeld theory

The electric potential and the electromagnetic field for a linearly accelerated Born–Infeld charged particle are obtained in an inertial frame by a method that can, in principle, be applied to any electromagnetic theory. The method is based on (i) the fact that the metric near the horizon of a Schwarzschild black hole is equivalent to that of Rindler spacetime, and (ii) a theorem that guarantees that the electrostatic potential for a given nonlinear theory in a static, spherically symmetric spacetime is entirely specified by the Maxwellian electrostatic potential in the same background. Using analytical and numerical methods, the features of the radiation field and the radiation-reaction for such an accelerated particle are discussed in detail.

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.

Nonlinear problems inspired by the Born–Infeld theory of electrodynamics

Abstract It is shown that nonlinear electrodynamics of the Born–Infeld theory type may be exploited to shed insight into a few fundamental problems in theoretical physics, including rendering electromagnetic asymmetry to energetically exclude magnetic monopoles, achieving finite electromagnetic energy to relegate curvature singularities of charged black holes, and providing theoretical interpretation of equations of state of cosmic fluids via k-essence cosmology. Also discussed are some nonlinear differential equation problems.

Non-linear electrodynamics from massive gravity

As a counterpart to the four-fermion interaction, which describes massive vector exchange at low energies, we investigate the low energy effective action of photons under exchange of a massive graviton. We show how integrating out a massive graviton leads to the most general duality-invariant vector interactions in 4D or, vice versa, how any such interactions have a natural interpretation within massive gravity. Moreover, we demonstrate how the special case of Born-Infeld theory arises from arguably the simplest graviton potential within ghost-free dRGT massive gravity.

Existence of high energy solutions for superlinear coupled Klein-Gordons and Born-Infeld equations

In this article, we study the system of Klein-Gordon and Born-Infeld equations $$\displaylines{ -\Delta u +V(x)u-(2\omega+\phi)\phi u =f(x,u), \quad x\in \mathbb{R}^3,\cr \Delta \phi+\beta\Delta_4\phi=4\pi(\omega+\phi)u^2, \quad x\in \mathbb{R}^3, }$$ where \(\Delta_4\phi=\hbox{div}(|\nabla\phi|^2\nabla\phi)$\), \(\omega\) is a positive constant. Assuming that the primitive of \(f(x,u)\) is of 2-superlinear growth in \(u\) at infinity, we prove the existence of multiple solutions using the fountain theorem. Here the potential \(V\) are allowed to be a sign-changing function. For more information see https://ejde.math.txstate.edu/Volumes/2024/18/abstr.html

Formulation of Galilean relativistic Born–Infeld theory

In this paper, we formulate, for the first time, in a systematic manner, Galilean relativistic Born–Infeld action in detail. Exploiting maps connecting Lorentz relativistic and Galilean relativistic vectors, we construct the two limits (electric and magnetic) of Galilean relativistic Born–Infeld action from usual relativistic Born–Infeld theory. An action formalism is thereby derived. From this action, equations of motion are obtained either in the potential or field formulation. Galilean version of duality transformations involving the electric and magnetic fields are defined. They map the electric limit relations to the magnetic ones and vice-versa, exactly as happens for Galilean relativistic Maxwell theory. We also explicitly show the Galilean boost and gauge invariances of the theory in both limits.

Existence and Regularity for Prescribed Lorentzian Mean Curvature Hypersurfaces, and the Born–Infeld Model

Existence and Regularity for Prescribed Lorentzian Mean Curvature Hypersurfaces, and the Born–Infeld Model

$T \overline{T}$-like flows and $3d$ nonlinear supersymmetry

We show that the 3d3d Born-Infeld theory can be generated via an irrelevant deformation of the free Maxwell theory. The deforming operator is constructed from the energy-momentum tensor and includes a novel non-analytic contribution that resembles root-T \ overline{T}ToverlineT. We find that a similar operator deforms a free scalar into the scalar sector of the Dirac-Born-Infeld action, which describes transverse fluctuations of a D-brane, in any dimension. We also analyse trace flow equations and obtain flows for subtracted models driven by a relevant operator. In 3d3d, the irrelevant deformation can be made manifestly supersymmetric by presenting the flow equation in \mathcal{N} = 1𝒩=1 superspace, where the deforming operator is built from supercurrents. We demonstrate that two supersymmetric presentations of the D2-brane effective action, the Maxwell-Goldstone multiplet and the tensor-Goldstone multiplet, satisfy superspace flow equations driven by this supercurrent combination. To do this, we derive expressions for the supercurrents in general classes of vector and tensor/scalar models by directly solving the superspace conservation equations and also by coupling to \mathcal{N} = 1𝒩=1 supergravity. As both of these multiplets exhibit a second, spontaneously broken supersymmetry, this analysis provides further evidence for a connection between current-squared deformations and nonlinearly realized symmetries.

Asymptotic study of critical wave fronts for parameter-dependent Born–Infeld models: physically predicted behaviors and new phenomena

In this paper, we study some parameter-dependent reaction-diffusion models governed by the Born–Infeld (or Minkowski) operator. In dependence on two parameters , related to the field strength and to the diffusivity, we investigate the limit critical speed for traveling fronts, together with the limit behavior of the associated critical profiles. As the two main results, on the one hand we rigorously show that for arbitrarily large electric fields the critical speed and the critical profile converge to the ones of the linear diffusion problem, agreeing with the well-known physical prediction that, in this case, Born’s law and Maxwell’s law coincide. Such a result is accompanied by a counterpart for arbitrarily small electric fields and a complete analysis for vanishing/large diffusion. On the other hand, we prove the onset of a new and unexpected phenomenon for the singular perturbation problem: the critical speed of propagation does not converge to zero and, for KPP or combustion-type reactions, the limit front profile becomes sharp on one side only. In fact, this latter coincides with the C 1-gluing of a piecewise linear profile having slope equal to 1 when nonconstant, and of a regular inviscid profile propagating at the limit speed. The gluing point and the value of the limit speed are determined explicitly. The outcomes of the whole discussion, based on a careful analysis of the first-order reduction associated with the original equation, show substantial differences and peculiarities of the Born–Infeld operator with respect to linear or saturating diffusions, and are supported by several numerical experiments.

Existence of solutions for critical Klein–Gordon equations coupled with Born–Infeld theory in higher dimensions

In this paper, we investigate the existence of nontrivial solutions for nonlinear Klein–Gordon equations coupled with Born–Infeld theory with critical Sobolev exponents by variational methods.

On solutions for a class of Klein–Gordon equations coupled with Born–Infeld theory with Berestycki–Lions conditions on $ \mathbb{R}^3 $

<abstract><p>In this paper, the existence of multiple solutions for a class of Klein–Gordon equations coupled with Born–Infeld theory was investigated. The potential and the primitive of the nonlinearity in this kind of elliptic equations are both allowed to be sign-changing. Besides, we assumed that the nonlinearity satisfies the Berestycki–Lions type conditions. By employing Ekeland's variational principle, mountain pass theorem, Pohožaev identity, and various other techniques, two nontrivial solutions were obtained under some suitable conditions.</p></abstract>

Infinitely Many Solutions and a Ground-State Solution for Klein-Gordon Equation Coupled with Born-Infeld Theory

Infinitely Many Solutions and a Ground-State Solution for Klein-Gordon Equation Coupled with Born-Infeld Theory

Photon-photon scattering

The existence of photon-photon scattering historically was one of the first non-trivial predictions of QED. However, since the cross section is very small at low energies it was only in 2017 that a direct measurement was achieved in heavy-ion collisions at the LHC. After short reviews of the history of the subject and of the CERN experiment, I discuss the general structure of the four-photon tensor, which also serves as the prototype for all vertices of four gauge bosons. I then come to generalizations from QED to the Standard Model and beyond, in particular to the Born-Infeld theory that has gained some popularity in recent years as an alternative to standard quantum electrodynamics.