Born-Infeld Theory Research Articles

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.

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 .

Deflection light in strong field from global monopole in Eddington-inspired Born-Infeld gravity

We examine the deflection of light due to the gravitational field of global monopole in Eddington-inspired Born-Infeld theory using strong field approach, which accurately explains light deflection when the impact parameter is small. In this paper, we will discuss the deflection angle and the radius of the photon sphere. We discover that the global monopole will increase the deflection angle and the radius of the photon sphere (compared to Schwarzschild), while EiBI parameter will decrease the radius of the photon sphere and the decreasing of deflection angle is shown clearly with small impact parameter.

Bounce models within teleparallel modified gravity

In this paper, working in a Friedman-Lemaitre-Robertson-Walker (FLRW), first, in the flat case, we recover the generalized Friedman equation of Quantum Loop cosmology, and therefore the cosmological bounce, in the framework of modified teleparallel gravity $f(T)$-model, $T$ being the torsion scalar introduced in teleparallel gravity approach, without invoking unconventional exotic matter. Furthermore we study the associated perturbations again in a flat FLRW space-time. Then, we generalize the results to the curved FLRW space-time, where some issues related to the choice of tetrad exist, by using an appropriate formulation. In this context, the results of Born-Infeld model are also investigated.

Rotating and charged Gauss–Bonnet BTZ black holes

We obtain charged and rotating black hole solutions to the novel 3D Gauss–Bonnet theory of gravity recently proposed, both of which generalize the Banados–Teitelboim–Zanelli (BTZ) metric. The charged solutions are obtained in the Maxwell and Born–Infeld theories and feature ‘universal thermodynamics’—identical to the thermodynamics of their Einstein cousins. The rotating Gauss–Bonnet BTZ black holes are quite exceptional and are not of constant curvature. They possess an ergoregion and outer horizon, but do not have an inner horizon. We present their basic properties and show that they break the universality of thermodynamics present for their static charged counterparts. Extending our considerations to higher dimensions, we also obtain novel 4D Gauss–Bonnet rotating black strings.

Nonlinear duality-invariant conformal extension of Maxwell’s equations

All nonlinear extensions of the source-free Maxwell equations preserving both SO(2) electromagnetic duality invariance and conformal invariance are found, and shown to be limits of a one-parameter generalisation of Born-Infeld electrodynamics. The strong-field limit is the same as that found by Bialynicki-Birula from Born-Infeld theory but the weak-field limit is a new one-parameter extension of Maxwell electrodynamics, which is interacting but admits exact light-velocity plane-wave solutions of arbitrary polarisation. Small-amplitude waves on a constant uniform electromagnetic background exhibit birefringence, but one polarisation mode remains lightlike.

Standing wave solutions in Born–Infeld theory

We study standing-wave solutions of Born–Infeld electrodynamics, with nonzero electromagnetic field in a region between two parallel conducting plates. We consider the simplest case which occurs when the vector potential describing the electromagnetic field has only one nonzero component depending on time and on the coordinate perpendicular to the plates. The problem then reduces to solving the scalar Born–Infeld equation, a nonlinear partial differential equation in 1+1 dimensions. We apply two alternative methods to obtain standing-wave solutions to the Born–Infeld equation: an iterative method, and a “minimal surface” method. We also study standing wave solutions in a uniform constant magnetic field background. The results obtained in this work provide a theoretical background for experimental tests of Born–Infeld theory.

Generalised Schwarzschild metric from double copy of point-like charge solution in Born-Infeld theory

We discuss possible application of the classical double copy procedure to construction of a generalisation of the Schwarzschild metric starting from an α′-corrected open string analogue of the Coulomb solution. The latter is approximated by a point-like charge solution of the Born-Infeld action, which represents the open string effective action for an abelian vector field in the limit when derivatives of the field strength are small. The Born-Infeld solution has a regular electric field which is constant near the origin suggesting that corrections from the derivative terms in the open string effective action may be small there. The generalization of the Schwarschild metric obtained by the double copy construction from the Born-Infeld solution looks non-singular but the corresponding curvature invariants still blow up at r=0. We discuss the origin of this singularity and comment on possible generalizations.

Stability of magnetic black holes in general nonlinear electrodynamics

We study the perturbative stability of magnetic black holes in a general class of nonlinear electrodynamics, where the Lagrangian is given by a general function of the field strength of electromagnetic field $F_{\mu\nu}$ and its Hodge dual $\widetilde{F}_{\mu\nu}$. We derive sufficient conditions for the stability of the black holes. We apply the stability conditions to Bardeen's regular black holes, black holes in Euler-Heisenberg theory, and black holes in Born-Infeld theory. As a result, we obtain a sufficient condition for the stability of Bardeen's black holes, which restricts $F_{\mu\nu}\widetilde{F}^{\mu\nu}$ dependence of the Lagrangian. We also show that black holes in Euler-Heisenberg theory are stable for a sufficiently small magnetic charge. Moreover, we prove the stability of black holes in the Born-Infeld electrodynamics even when including $F_{\mu\nu}\widetilde{F}^{\mu\nu}$ dependence.

Equilibrium measures and equilibrium potentials in the Born-Infeld model

In this paper, we consider the electrostatic Born-Infeld model(BI){−div(∇ϕ1−|∇ϕ|2)=ρin RN,lim|x|→∞⁡ϕ(x)=0 where ρ is a charge distribution on the boundary of a bounded domain Ω⊂RN, with N⩾3. We are interested in its equilibrium measures, i.e. charge distributions which minimize the electrostatic energy of the corresponding potential among all possible distributions with fixed total charge. We prove existence of equilibrium measures and we show that the corresponding equilibrium potential is unique and constant in Ω‾. Furthermore, for smooth domains, we obtain the uniqueness of the equilibrium measure, we give its precise expression, and we verify that the equilibrium potential solves (BI). Finally we characterize balls in RN as the unique sets among all bounded C2,α-domains Ω for which the equilibrium distribution is a constant multiple of the surface measure on ∂Ω. The same results are obtained also for Taylor approximations of the electrostatic energy.

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.

Explicit self-similar solutions for a class of zero mean curvature equation and minimal surface equation

In this paper, we consider the existence of self-similar solution for a class of zero mean curvature equations including the Born–Infeld equation, the membrane equation and maximal surface equation. By Calabi’s correspondence, this also gives a family of explicit self-similar solutions for the minimal surface equation. Those models arise in string theory and geometric minimal surfaces theory. Moreover, we construct a family of instanton metric obtained from new exact singular solutions for minimal surfaces by noticing the correspondence between minimal surfaces in the three dimensional Euclidean space and gravitational instantons possessing two killing vectors.

Strong cosmic censorship for a scalar field in a logarithmic-de Sitter black hole

It has been shown that the quasinormal modes of perturebated fields can be used to investigate the validity of strong cosmic censorship (SCC). Relevant issues for Reissner–Nordstrom–de Sitter (RN-dS) black holes and Born–Infeld–de Sitter black holes have been discussed. In this paper, we investigate SCC in an asymptotic RN-dS black hole with logarithmic nonlinear electromagnetic field perturbed by massless scalar fields. It has been argued that SCC can be violated in a near-extremal RN-dS black hole. However, we find that the NLED effect can rescue SCC for a near-extremal logarithmic-de Sitter black hole. Compared with Born-Infeld model, we find that the NLED effect has similar behavior.

All-multiplicity one-loop amplitudes in Born-Infeld electrodynamics from generalized unitarity

We initiate a study of non-supersymmetric Born-Infeld electrodynamics in 4d at the quantum level. Explicit all-multiplicity expressions are calculated for the purely rational one-loop amplitudes in the self-dual (+ + … +) and next-to-self-dual (− + … +) helicity sectors. Using a supersymmetric decomposition, d-dimensional unitarity cuts of the integrand factorize into tree-amplitudes in a 4d model of Born-Infeld photons coupled to a massive complex scalar. The two-scalar tree-amplitudes needed to construct the Born-Infeld integrand are computed using two complimentary approaches: (1) as a double-copy of Yang-Mills coupled to a massive adjoint scalar with a dimensionally reduced form of Chiral Perturbation Theory, and (2) by imposing consistency with low-energy theorems under a reduction from 4d to 3d and T-duality. The Born-Infeld integrand is integrated in d = 4 − 2ϵ dimensions at order mathcal{O}left({in}^0right) using the dimension-shifting formalism. We comment on the implications for electromagnetic duality in quantum Born-Infeld theory.

Schwarzschild spacetime immersed in test nonlinear electromagnetic fields

Kerr black hole immersed in test, asymptotically homogeneous magnetic field, aligned along the symmetry axis, is described by Wald’s solution. We show how the static case of this solution may be generalized for nonlinear electromagnetic models via perturbative approach. Using this technique we find the lowest order correction to Wald’s solution on Schwarzschild spacetime in Euler–Heisenberg and Born–Infeld theories. Finally, we discuss the problem of highly conducting star in asymptotically homogeneous magnetic field.

Non-linear supersymmetry and Toverline{T} -like flows

The Toverline{T} deformation of a supersymmetric two-dimensional theory preserves the original supersymmetry. Moreover, in several interesting cases the deformed theory possesses additional non-linearly realized supersymmetries. We show this for certain mathcal{N} = (2, 2) models in two dimensions, where we observe an intriguing similarity with known mathcal{N} = 1 models in four dimensions. This suggests that higher-dimensional models with non-linearly realized supersymmetries might also be obtained from Toverline{T} -like flow equations. We show that in four dimensions this is indeed the case for mathcal{N} = 1 Born-Infeld theory, as well as for the Goldstino action for spontaneously broken mathcal{N} = 1 supersymmetry.

DBI in the IR

The infra-red limit of a planar static D3-brane in AdS is a tensionless D3-brane at the anti-de Sitter horizon with dynamics governed by a strong-field limit of the Dirac–Born–Infeld action, analogous to that found from the Born–Infeld action by Bialynicki-Birula. As in that case, the field equations are those of an interacting 4D conformal invariant field theory with an electromagnetic duality invariance, but the D3-brane origin makes these properties manifest. We also find an -invariant action for these equations.

Gravitino condensate in N = 1 supergravity coupled to the N = 1 supersymmetric Born–Infeld theory

Abstract The $N=1$ supersymmetric Born–Infeld theory coupled to $N=1$ supergravity in four spacetime dimensions is studied in the presence of a cosmological term with spontaneous supersymmetry breaking. The consistency is achieved by compensating a negative contribution to the cosmological term from the Born–Infeld theory by a positive contribution originating from the gravitino condensate. This leads to an identification of the Born–Infeld scale with the supersymmetry-breaking scale. The dynamical formation of the gravitino condensate in supergravity is reconsidered and the induced one-loop effective potential is derived. Slow-roll cosmological inflation with the gravitino condensate as the inflaton (near the maximum of the effective potential) is viable against the Planck 2018 data and can lead to the inflationary (Hubble) scale as high as $10^{12}$ GeV. Uplifting the Minkowski vacuum (after inflation) to a de Sitter vacuum (dark energy) is possible by the use of the alternative Fayet–Iliopoulos term. Some major physical consequences of our scenario for reheating are also briefly discussed.

Black hole magnetospheres in the Born–Infeld theory

We study the force-free electrodynamics on rotating black holes in the Born–Infeld (BI) effective theory. The stream equation describing a steady and axisymmetric magnetosphere is derived. From its near-horizon behavior, we obtain the modified Znajek regularity condition, with which we find that the horizon resistivity in the BI theory is generally not a constant. As expected, the outer boundary condition far away from the hole remains unchanged. In terms of the conditions at both boundaries, we derive the perturbative solution of split monopole in the slow rotation limit. It is interesting to realize that the correction to the solution relies not only on the parameter in the BI theory, but also on the radius (or the mass) of the hole. We also show that the quantum effects can undermine the energy extraction process of the magnetosphere in the nonlinear theory and the extraction rate gets the maximum in the Maxwell theory.

Solitary wave of ground state type for a nonlinear Klein–Gordon equation coupled with Born–Infeld theory in ℝ2

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