Search Results (18)

A new conformally invariant gravitational generalization of the Born–Infeld (BI) model is proposed and analyzed from the point of view of symmetries. Taking a geometric identity involving the determinant functions det$f\left(B_{\mu \nu },F_{\mu \nu }\right)$ with the Bach $B_{\mu \nu }$ and the electromagnetic field $F_{\mu \nu }$ tensors (with the 4-dimensional Greek letter indexes), two characteristic geometrical Lagrangian densities (Lagrangians) are derived: the first Lagrangian being the square root of the determinant function $\sqrt{\left|det\left(B_{\mu \nu }+F_{\mu \nu }\right)\right|}$ (reminiscent of the standard BI model) and the second Lagrangian being the fourth root $\sqrt[4]{gdet\left(B_{\alpha \gamma }{B}_{\beta }^{\gamma }+F_{\alpha \gamma }{F}_{\beta }^{\gamma }\right)}$. It is shown, after explicit computation of the gravitational equations, that the square-root model is incompatible with the inclusion of the electromagnetic tensor, consequently forcing the nullity of $F_{\mu \nu }$. In sharp contrast, the traceless fourth-root model is fully compatible and a natural ansatz of the type $B_{\mu \rho }{B}_{\nu }^{\rho }\propto \mathrm{\Omega }\left(x\right)g_{\mu \nu }$ (conformal-Killing), with $\mathrm{\Omega }$ the conformal factor and x the 4-coordinate, can be considered. Among other essential properties, the geometrical conformal Lagrangian of the fourth-root type is self-similar with respect to the determinant g of the metric tensor $g_{\mu \nu }$ and can be extended to non-Abelian fields in a way similar to the model developed by the author earlier. This self-similarity is related to the conformal properties of the model, such as the Bach currents or flows presumably of a topological origin. Possible applications and comparisons with other models are briefly discussed. Full article

In this paper we discuss some results on the existence of solutions for an elliptic system appearing in physical sciences. In particular the system appears when we look at standing wave solutions in the electrostatic situation for the Schrödinger equation coupled, with the minimal coupling rule, with the electromagnetic equations of Born–Infeld theory. Many difficulties appear, especially due to the fact we are in an unbounded domain (the whole space ${\mathbb{R}}^3$) and to the intrinsic nonlinear nature of the equations. We are able to prove the existence of a minimal energy solution by showing an approximating procedure that can be adapted depending on the value of the parameter p, which is in the nonlinearity. Full article

We investigate in this paper the static radial coordinate-dependent spherically symmetric spacetime in teleparallel $F\left(T\right)$ gravity for a scalar field source. We begin by setting the static field equations (FEs) to be solved and solve the conservation laws for scalar field potential solutions. We simplify the FEs and then find a general formula for computing the new teleparallel $F\left(T\right)$ solutions applicable for any scalar field potential $V\left(T\right)$ and coframe ansatz. We compute new non-trivial teleparallel $F\left(T\right)$ solutions by using a power-law coframe ansatz for each scalar potential case arising from the conservation laws. We apply this formula to find new exact teleparallel $F\left(T\right)$ solutions for several cases of coframe ansatz parameter. The new $F\left(T\right)$ solution classes will be relevant for studying the models close to Born–Infeld and/or scalarized Black Hole (BH) solutions inside the dark energy (DE) described by a fundamental scalar field such as quintessence, phantom energy or quintom system, to name only those types. Full article

We compute the evolution of linear perturbations on top of a background solution of a general nonlinear electromagnetic theory. This evolution can be described in terms of two effective metrics, and we analyze under what conditions they are conformally related so that they can be regarded as analog models of non-trivial gravitational fields in the eikonal approximation. This is the case in Born–Infeld theory. For the background created by a static point electric charge in the Born–Infeld theory, the effective metric describes a wormhole geometry for light rays. Depending on the impact parameter, incoming light rays are either scattered to infinity or approach the wormhole slowing down their pace until they hit the charge at vanishing speed. The same effective wormhole geometry is obtained for a magnetic monopole and a dyon and we relate it to the duality invariance of Born–Infeld electromagnetism. Finally, we analyze the scalar Dirac–Born–Infeld theory and show that the effective wormhole geometry is not generated by a particle with scalar charge. Full article

We apply a very simple procedure to construct non-singular cosmological models for flat Friedmann universes filled with minimally coupled scalar fields or by tachyon Born–Infeld-type fields. Remarkably, for the minimally coupled scalar field and the tachyon field, the regularity of the cosmological evolution, or in other words, the existence of bounce, implies the necessity of the transition between scalar fields with standard kinetic terms to those with phantom ones. In both cases, the potentials in the vicinity of the point of the transition have a non-analyticity of the cusp form that is characterized by the same exponent and is equal to $\frac{2}{3}$. If, in the tachyon model’s evolution, the pressure changes its sign, then another transformation of the Born–Infeld-type field occurs: the tachyon transforms into a pseudotachyon, and vice versa. We also undertake an analysis of the stability of the cosmological evolution in our models; we rely on the study of the speed of sound squared. Full article

In this paper, by treating the cosmological constant as a thermodynamic pressure, we study the thermodynamics and phase transitions of the dyonic AdS black holes in Gauss-Bonnet-Scalar gravity, where the conformal scalar field is considered. In a more general extended phase space, we first verified the first law of black hole thermodynamics, and find that it is always true. Meanwhile, the corresponding Smarr relation is also obtained. Then, we found that this black hole exhibits interesting critical behaviors in six dimensions, i.e., two swallowtails can be observed simultaneously. Interestingly, in a specific parameter space, we observed the small/intermediate/large black hole phase transitions, with the triple point naturally appearing. Additionally, the small/large black hole phase transition, similar to the liquid/gas phase transition of the van der Waals fluids, can also be found in other parameter regions. Moreover, we note that the novel phase structure composed of two separate coexistence curves discovered in the dyonic AdS black holes in Einstein-Born-Infeld gravity disappears in Gauss-Bonnet-Scalar gravity. This suggests that this novel phase structure may be related to gravity theory, and importantly, it is generally observed that the triple point is a universal property of dyonic AdS black holes. On the other hand, we calculated the critical exponents near the critical points and found that they share the same values as in mean field theory. Finally, it is true that these results will provide some deep insights into the interesting thermodynamic properties of the dyonic AdS black holes in the background of conformal scalar fields. Full article

We compute the weak bending angle of light within generalised Born–Infeld electrodynamics as it passes through the equatorial plane of a magnetic dipole. We start by considering the refractive index associated with the dipole within generalised Born–Infeld electrodynamics. Then, we calculate the Gaussian optical curvature based on these refractive indices. Using the Gauss–Bonnet theorem, we derive a formula to quantify the deflection angle in the presence of a strong magnetic field from a dipole. Our results align with results obtained through traditional geometric optics techniques, underscoring the importance of the Gauss–Bonnet theorem as a versatile tool for solving intricate problems in modern theoretical research. We apply our theoretical deflection angle formula to estimate the light bending in magnetars listed in the McGill catalogue, providing insights into the behaviour of light in environments with strong magnetic fields. Full article

This article investigates the radial and non-radial geodesic structures of the generalized K-essence Vaidya spacetime. Within the framework of K-essence geometry, it is important to note that the metric does not possess conformal equivalence to the conventional gravitational metric. This study employs a non-canonical action of the Dirac–Born–Infeld kind. In this work, we categorize the generalized K-essence Vaidya mass function into two distinct forms. Both the forms of the mass functions have been extensively utilized to analyze the radial and non-radial time-like or null geodesics in great detail inside the comoving plane. Indications of the existence of wormholes can be noted during the extreme phases of spacetime, particularly in relation to black holes and white holes, which resemble the Einstein–Rosen bridge. In addition, we have also detected a distinctive indication of the quantum tunneling phenomenon around the singularity ($r\to 0$). Furthermore, we have found that for certain types of solutions, there exist circular orbits through the event horizon as well as quasicircular orbits. Also, we have noted that there is no central singularity in our spacetime where both r and t tend towards zero. The existence of a central singularity is essential for any generalized Vaidya spacetime. This indicates that spacetime can be geodesically complete, which correlates with the findings of Kerr’s recent work (2023). Full article

We determine the k-essence Lagrangian of a relativistic barotropic fluid. The equation of state of the fluid can be specified in different manners depending on whether the pressure is expressed in terms of the energy density (model I), the rest-mass density (model II), or the pseudo rest-mass density for a complex scalar field in the Thomas-Fermi approximation (model III). In the nonrelativistic limit, these three formulations coincide. In the relativistic regime, they lead to different models that we study exhaustively. We provide general results valid for an arbitrary equation of state and show how the different models are connected to each other. For illustration, we specifically consider polytropic and logotropic dark fluids that have been proposed as unified dark matter and dark energy models. We recover the Born-Infeld action of the Chaplygin gas in models I and III and obtain the explicit expression of the reduced action of the logotropic dark fluid in models II and III. We also derive the two-fluid representation of the Chaplygin and logotropic models. Our general formalism can be applied to many other situations such as Bose-Einstein condensates with a ${\left|\phi \right|}^4$ (or more general) self-interaction, dark matter superfluids, and mixed models. Full article

We revisit universal features of duality in linear and nonlinear relativistic scalar and Abelian 1-form theories with single or multiple fields, which exhibit ordinary or generalized global symmetries. We show that such global symmetries can be interpreted as generalized Killing isometries on a suitable, possibly graded, target space of fields or its jet space when the theory contains higher derivatives. This is realized via a generalized sigma model perspective motivated from the fact that higher spin particles can be Nambu–Goldstone bosons of spontaneously broken generalized global symmetries. We work out in detail the 2D examples of a compact scalar and the massless Heisenberg pion fireball model and the 4D examples of Maxwell, Born–Infeld, and ModMax electrodynamics. In all cases we identify the ’t Hooft anomaly that obstructs the simultaneous gauging of both global symmetries and confirm the anomaly matching under duality. These results readily generalize to higher gauge theories for p-forms. For multifield theories, we discuss the transformation of couplings under duality as two sets of Buscher rules for even or odd differential forms. Full article

The early cosmology, driven by a single scalar field, both massless and massive, in the context of Eddington-inspired Born-Infeld gravity, is explored. We show the existence of nonsingular solutions of bouncing and loitering type (depending on the sign of the gravitational theory’s parameter, $ϵ$) replacing the Big Bang singularity, and discuss their properties. In addition, in the massive case, we find some new features of the cosmological evolution depending on the value of the mass parameter, including asymmetries in the expansion/contraction phases, or a continuous transition between a contracting phase to an expanding one via an intermediate loitering phase. We also provide a combined analysis of cosmic chronometers, standard candles, BAO, and CMB data to constrain the model, finding that for roughly $\left|ϵ\right|\lesssim 5·{10}^{-8}{\mathrm{m}}^2$ the model is compatible with the latest observations while successfully removing the Big Bang singularity. This bound is several orders of magnitude stronger than the most stringent constraints currently available in the literature. Full article

Killing vector fields can be used as gauge vector potentials since the associated electromagnetic field tensor automatically satisfies the source-free Maxwell’s equations in vacuum spacetimes. This fact enabled Wald to find the form of the electromagnetic tensor corresponding to the Kerr black hole immersed in a uniform test magnetic field. We present the generalisation of this result, which is valid for static black holes surrounded by nonlinear electromagnetic fields. The first obstacle we encountered when dealing with the nonlinear electrodynamics was that the above-described ansatz no longer works. Secondly, finding the exact solution in a closed form proved to be a rather challenging task because it would require solving a highly nonlinear differential equation. The alternative approach is via perturbative expansion around the original Wald’s solution. We obtain the equation which determines the lowest order correction to the gauge vector field 1-form and magnetic scalar potential. With the main focus on the Born–Infeld and Euler–Heisenberg theories on the Schwarzschild background, we calculate the aforementioned correction. Additionally, we show that this perturbative correction does not change electric and magnetic Komar charges or the asymptotic behaviour of the field. Finally, stating physical arguments, we justify the usage of the perturbative approach. Full article

On extending the Standard Model (SM) Lagrangian, through a non-linear Born–Infeld (BI) hypercharge term with a parameter $\beta$ (of dimensions of [mass] ${}^2$ ), a finite energy monopole solution was claimed by Arunasalam and Kobakhidze. We report on a new class of solutions within this framework that was missed in the earlier analysis. This new class was discovered on performing consistent analytic asymptotic analyses of the nonlinear differential equations describing the model; the shooting method used in numerical solutions to boundary value problems for ordinary differential equations is replaced in our approach by a method that uses diagonal Padé approximants. Our work uses the ansatz proposed by Cho and Maison to generate a static and spherically-symmetric monopole with finite energy and differs from that used in the solution of Arunasalam and Kobakhidze. Estimates of the total energy of the monopole are given, and detection prospects at colliders are briefly discussed. Full article

We propose the supersymmetric extension of the modified Born–Infeld-axion-dilaton non-linear electrodynamics that has confined static abelian solutions used for describing the electromagnetic confinement in the presence of axion and dilaton fields, as well as charged matter. The supersymmetric extension also has the non-trivial scalar potential that implies the upper bounds on the matter fields. Full article

The Eddington-inspired-Born-Infeld (EiBI) model is reformulated within the mimetic approach. In the presence of a mimetic field, the model contains non-trivial vacuum solutions. We study a realistic primordial vacuum universe and we prove the existence of regular solutions. Besides, the linear instabilities in the EiBI model are found to be avoidable for some bouncing solutions. For a vacuum, static and spherically symmetric geometry, a new branch of solutions in which the black hole singularity that is replaced with a lightlike singularity is found. Full article