Born-Infeld Theory Research Articles

On the Classification of Symmetry Reductions and Invariant Solutions for the Euler–Lagrange–Born–Infeld Equation

We study a connection between the structural properties of the low-dimension (dimL ≤ 3) nonconjugate subalgebras of the Lie argebra of the generalized Poincar´e group P(1,4) and the results of symmetry reductions for the Euler–Lagrange–Born–Infeld equation. We have performed the classification of nonsingular manifolds in the space M(1 , 3 ) × R(u) invariant with respect to three-dimensional nonconjugate subalgebras of the Lie algebra of the group P(1,4). The results are used for the classification of symmetry reductions and invariant solutions of the Euler–Lagrange–Born–Infeld equation.

Infinitely Many Solutions for the Klein–Gordon Equation with Sublinear Nonlinearity Coupled with Born–Infeld Theory

This paper is concerned with the following Klein–Gordon equation with sublinear nonlinearity coupled with Born–Infeld theory: $$\begin{aligned} \left\{ \begin{array}{ll} \displaystyle -\Delta u+ V(x)u-(2\omega +\phi )\phi u=f(x,u), &{}\quad x\in {\mathbb {R}}^{3},\\ \Delta \phi +\beta \Delta _{4}\phi =4\pi (\omega +\phi )u^{2},&{}\quad x\in {\mathbb {R}}^{3}. \end{array} \right. \end{aligned}$$ Under some appropriate assumptions on V(x) and f(x, u), we prove the existence of infinitely many negative-energy solutions for the above system via the genus properties in critical point theory. Some recent results from the literature are improved and extended.

Ricci-Based Gravity theories and their impact on Maxwell and nonlinear electromagnetic models

We extend the correspondence between metric-affine Ricci-Based Gravity the- ories and General Relativity (GR) to the case in which the matter sector is represented by linear and nonlinear electromagnetic fields. This complements previous studies focused on fluids and scalar fields. We establish the general algorithm that relates the matter fields in the GR and RBG frames and consider some applications. In particular, we find that the so-called Eddington-inspired Born-Infeld gravity theory coupled to Maxwell electromag- netism is in direct correspondence with GR coupled to Born-Infeld electromagnetism. We comment on the potential phenomenological implications of this relation.

Meissner effect in holographic superconductors with Dirac–Born–Infeld electrodynamics

In this paper, we have investigated the Meissner effect of holographic superconductors in the presence of Dirac–Born–Infeld electrodynamics. The matching method is applied to obtain the critical magnetic field and the critical temperature. The critical magnetic field obtained from this investigation shows the effects of the DBI parameter [Formula: see text] and differs from that obtained from Born electrodynamics because of the extra [Formula: see text] term in the Dirac–Born–Infeld theory. It is observed that the critical magnetic field increases in Dirac–Born–Infeld theory compared to that in the Born theory.

Dynamical behavior near explicit self-similar blow–up solutions for the Born–Infeld equation

This paper studies the dynamical behavior near a new family of explicit self-similar solutions for the one-dimensional Born–Infeld equation. This quasilinear scalar field equation arises from nonlinear electromagnetism, as well as branes in string theory and minimal surfaces in Minkowski spacetimes. We show that both this model and the linear wave equation admit the same family of explicit timelike self-similar blow-up solutions; meanwhile, Lyapunov nonlinear stability of those self-similar blow-up solutions is given inside a strictly proper subset of the backward light cone.

Creation of the de sitter space from nothing in Eddington-inspired Born-Infeld theory

In this paper, we revisit Vilenkin’s “creation of universes from nothing” in the framework of the Eddington-inspired Born-Infeld (EiBI) theory of gravity. In Vilenkin solution, a de Sitter space universe is created by quantum tunneling process from nothing. We incorporate the EiBI theory into this model. We use two kinds of cosmological constants, one from the EiBI theory and another from the effective potential. The resulting action has a slight modification than the original one.

Unified web for expansions of amplitudes

In this paper, we demonstrate that using differential operators one can construct the complete unified web for expansions of amplitudes for a wide range of theories. We first re-derive the expansion of multi-trace Einstein-Yang-Mills amplitudes to Kleiss-Kuijf basis of color-ordered Yang-Mills amplitudes, by applying proper differential operators which modify the coefficients in the recursive expansion of single-trace Einstein- Yang-Mills amplitudes. Next, through differential operators which act on amplitudes only, we obtain expansions of amplitudes of Yang-Mills theory, Yang-Mills-scalar theory, ϕ4 theory, non-linear sigma model, bi-adjoint scalar theory, Born-Infeld theory, Dirac-Born-Infeld theory and special Galileon theory. Then, together with other results in literatures, the complete unified web is achieved. This web for expansions is the dual version of the unified web for differential operators. Thus, connections among amplitudes of a variety of theories, which are reflected by Cachazo-He-Yuan integrands and differential operators previously, can also be represented by expansions. We also find that amplitudes of all theories in the web can be expanded to double color-ordered bi-adjoint scalar amplitudes in the double copy formula.

Asymptotically-flat Black Hole in EiBI-Born-Infeld Theory

We study static spherically-symmetric solutions of charged Eddington-inspired Born-Infeld (EiBI) theory of gravity in asymptotically-flat D-dimensional spacetime. We consider nonlinear electrodynamics for the matter fields. In this particular work, the nonlinear theory we specifically consider is the Born-Infeld electrodynamics. We found that metrics can not be integrated in general dimensions. In order to solve it, we focus on studying on the case α ≡ 4κb2 = 1. We study the electric fields. We find that this theory produces finite electric fields for any dimension. In Ricci scalar calculations, we find only point singularity.

Chi-Squared test for constraining free parameters of modified Gravity on Brown Dwarfs

Constraining free parameters of two modified gravity theories such as beyond Horndeski and Eddington Inspired Born-Infeld Theories of Gravity have been done precisely with LHS6343C data. However, it remains insufficient to explain the radius and mass relation of Brown Dwarf globally. We still need to identify how well beyond Horndeski and Eddington Inspired Born-Infeld Theories of Gravity being compared by the completed observation mass-radius data of Bayliss et. al. The provided data gives error-bar that can be used to study more systematically through the standard deviation analysis. We do Chi-Squared test to obtain minimum value on the free parameters of both Modified Gravity theories. We compare the two results and constrain the free parameters of both theories on confidence level 1 σ. We can obtain the more accurate results for determining the limits of free parameters of both theories.

Overturning and apparent anisotropic pressure in Eddington-inspired Born-Infeld theory on compact stars

The advantage of mapping modified gravity theories with standard matter into general relativity (GR) with modified matter is that we can quickly implement the well-established analytical and numerical methods developed within GR to study modified gravity theories and compare the modified gravity theories with current observational data. In this paper, we explicitly show that overturning/cracking instability may occur in an isotropic Eddington-inspired Born-Infeld (EiBI) stellar structure. Analyses are done by reducing the Tolman-Oppenheimer-Volkoff-like equations of EiBI into the ones of GR with an additional anisotropiclike nonlinear term. We obtain the term by expanding the stellar structure equations with respect to $\ensuremath{\gamma}\ensuremath{\kappa}\ensuremath{\epsilon}$ and $\ensuremath{\gamma}\ensuremath{\kappa}P$ and by using numerical calculations. We find that, for a specific value of $\ensuremath{\kappa}$, the overturning/cracking may occur. In the nonrelativistic regime, cracking tends to occur when $\ensuremath{\kappa}g0$. In the relativistic regime, for neutron stars (NS) with equation of state (EOS) based on a relativistic mean field model (RMF), the overturning occurs at $\ensuremath{\kappa}\ensuremath{\gtrsim}0$, and the overturning point is located near the core of the star. We also show that the stellar structure equations within EiBI theory with isotropic matter can be recast into GR defined in a physical metric $g$ with a modified (apparent) anisotropic matter. In this representation, the signature of a potentially overturning instability within the apparent anisotropic structure is present and related to the asymptotic behavior of the apparent speed of sound near the center of the star and an imaginary value of the apparent tangential speed of sound near the edge of the star.

Component d = 6 Born-Infeld theory with N = (2, 0) \u2192 N = (1, 0) supersymmetry breaking

The formalism of nonlinear realizations is used to construct a theory with 1/2 partial breaking of global supersymmetry with the N = (1, 0), d = 6 abelian vector multiplet as a Goldstone superfield. Much like the case of the N = 2, d = 4 Born-Infeld theory, proper irreducibility conditions of the multiplet are selected by the invariance with respect to the external automorphisms of the Poincaré superalgebra. They are found in the lowest nontrivial order in the auxiliary field. The fermionic contributions to the Bianchi identity are restored by assuming its covariance with respect to broken supersymmetry. The invariance of the action with respect to unbroken supersymmetry is checked in the lowest order in the fermionic fields. The supersymmetry preserving reduction of the d = 6 action to four dimensions is performed, resulting in the N = 4, d = 4 Born-Infeld theory. As expected, the reduced action enjoys U(1) self-duality.

Palatini f(R,Lm,RμνTμν) gravity and its Born-Infeld semblance

We investigate Palatini $f(\mathcal{R},\mathcal{L}_m, \mathcal{R}_{\mu\nu}T^{\mu\nu})$ modified theories of gravity wherein the metric and affine connection are treated as independent dynamical fields and the gravitational Lagrangian is made a function of the Ricci scalar $\mathcal{R}$, the matter Lagrangian density $\mathcal{L}_m,$ and a "matter-curvature scalar" $\mathcal{R}_{\mu\nu}T^{\mu\nu}$. The field equations and the equations of motion for massive test particles are derived, and we show that the independent connection can be expressed as the Levi-Civita connection of an auxiliary, energy-momentum dependent metric, related to the physical metric by a matrix transformation. Similar to metric $f(\mathcal{R}, T, \mathcal{R}_{\mu\nu}T^{\mu\nu})$ gravity, the field equations impose the non-conservation of the energy-momentum tensor, leading to an appearance of an extra force on massive test particles. We obtain the explicit form of the field equations for massive test particles in the case of a perfect fluid, and an expression for the extra force. The nontrivial modifications to scalar fields and both linear and nonlinear electrodynamics are also considered. Finally, we detail the conditions under which the present theory is equivalent to the Eddington-inspired Born-Infeld (EiBI) model.

Infinitely many solutions and least energy solutions for Klein–Gordon equation coupled with Born–Infeld theory

ABSTRACTIn this paper, we prove the existence of infinitely many solutions and least energy solutions for the following nonhomogeneous Klein-Gordon equation coupled with Born-Infeld theory where is a constant, and is super-linear. Our results extend and improve the previous ones in the literature.

Critical phenomena of Born-Infeld-de Sitter black holes in cavities

We examine the thermodynamic behaviour of charged, asymptotically de Sitter black holes embedded in a finite-radius isothermal cavity, with a Born-Infeld gauge field replacing the ordinary Maxwell field. We find that the non-linearities of Born-Infeld theory lead to the presence of reentrant phase transitions in the canonical ensemble, whose existence and character are determined by the maximal electric field strength of the theory. We also examine the phase structure in the grand canonical ensemble, and demonstrate the presence of a new reentrant phase transition from radiation, to an intermediate size black hole, and back to radiation.

Wick rotations of solutions to the minimal surface equation, the zero mean curvature equation and the Born–Infeld equation

In this paper we investigate relations between solutions to the minimal surface equation in Euclidean $3$-space $\mathbb{E}^3$, the zero mean curvature equation in Lorentz-Minkowski $3$-space $\mathbb{L}^3$ and the Born-Infeld equation under Wick rotations. We prove that the existence conditions of real solutions and imaginary solutions after Wick rotations are written by symmetries of solutions, and reveal how real and imaginary solutions are transformed under Wick rotations. We also give a transformation theory for zero mean curvature surfaces containing lightlike lines with some symmetries. As an application, we give new correspondences among some solutions to the above equations by using the non-commutativity between Wick rotations and isometries in the ambient space.

Charged black holes in higher-dimensional Eddington-inspired Born-Infeld gravity

We study static (electrically)-charged solutions of Eddington-inspired Born-Infeld (EiBI) theory of gravity in general D-dimensional spacetime. We consider both linear (Maxwell) as well as nonlinear electrodynamics for the matter fields. In this particular work, the nonlinear theory we specifically consider is the Born-Infeld (BI) electrodynamics. The solutions describe higher-dimensional black holes in EiBI gravity. For the linear Maxwell field, we show that the electric field is still singular for D>4. This singularity is cured when EiBI is coupled to the BI electrodynamics. We obtain EiBI-BI black hole solutions in the limit of α˜≡4κb2/λ=1 and 2. We also investigate their thermodynamical property. We show that all solutions satisfy the first-law of black hole thermodynamics, from which their corresponding ADM mass can be extracted. It is found that κ imposes a charge screening that makes the corresponding Hawking temperature experiences some sudden jump from charged-type to the Schwarzschild-type at some critical value of κ. Thermodynamical stability reveals that the EiBI-BI black holes can exist with smaller horizon than their Reissner-Nordstrom (RN) counterparts.

The Bäcklund Transform and a New Exact Solution of the Born–Infeld Model

We present the Lagrangian and Hamiltonian of the Born–Infeld model in Cartesian and light cone variables. Using the auto-Backlund transformation, we construct new solutions of the corresponding nonlinear equation. In particular, a “dressed” Barbashov–Chernikov solution is obtained. Bibliography: 18 titles.

On a Yang-Mills Type Functional

We study a functional that derives from the classical Yang-Mills functional and Born-Infeld theory. We establish its first variation formula and prove the existence of critical points. We also obtain the second variation formula.

Supersymmetric Born-Infeld actions and new Fayet-Iliopoulos terms

We consider mathcal{N} = 1 supersymmetric Born-Infeld actions that have a second non-linear supersymmetry. We focus on the model proposed by Bagger and Galperin and show that the breaking of the second supersymmetry is sourced by the new Fayet-Iliopoulos D-term. Interpreting such an action as the effective theory of a space-filling (anti) D3-brane leads to an expression for the new Fayet-Iliopoulos parameter in terms of the brane tension and α′.

Born–Infeld Gravity from the MacDowell–Mansouri Action and Its Associated $${\varvec{\beta }}$$ β -Term

In this work a generalization of a Born–Infeld theory of gravity with a topological $$\beta $$ -term is proposed. These type of Born–Infeld actions were found from the theory introduced by MacDowell and Mansouri. This theory known as MacDowell–Mansouri (MM) gravity was one of the first attempts to construct a gauge theory of gravitation, and within this framework it was introduced in the action a topological $$\beta $$ -term relevant for quantization purposes in an analogous way as in Yang–Mills theory. By the use of the self-dual and antiself-dual actions of MM gravity, we further define a Born–Infeld gravity generalization corresponding to MM gravity with the $$\beta $$ -term.