Born-Infeld Electrodynamics Research Articles

Thermodynamical structure of AdS black holes in massive gravity with stringy gauge-gravity corrections

Motivated by gauge/gravity group in the low energy effective theory of the heterotic string theory and novel aspects of massive gravity in the context of lattice physics, the minimal coupling of Gauss–Bonnet-massive gravity with Born–Infeld electrodynamics is considered. At first, the metric function is calculated and then the geometrical properties of the solutions are investigated. It is found that there is an essential singularity at the origin and the intrinsic curvature is regular elsewhere. In addition, the effects of massive parameters are studied and black hole solutions with multi horizons are found in this gravity. Also, the conserved and thermodynamic quantities are calculated, and it is shown that the solutions satisfy the first law of thermodynamics. Furthermore, using heat capacity of these black holes, thermal stability and phase transitions are investigated. The variation of different parameters and related modifications on the (number of) phase transition are examined. Next, the critical behavior of the Gauss–Bonnet–Born–Infeld-massive black holes in the context of extended phase space is studied. It is shown how the variation of the different parameters affects the existence and absence of phase transition. Also, it is found that for specific values of different parameters, these black holes may enjoy the existence of a new type of phase transition which to our knowledge was not observed in black hole physics before.

Holographic paramagnetism–ferromagnetism phase transition in the Born–Infeld electrodynamics

In the probe limit, we investigate the effects of the Born–Infeld electrodynamics on the holographic paramagnetism–ferromagnetism phase transition in the background of a Schwarzschild–AdS black hole spacetime. We find that the presence of Born–Infeld scale parameter b decreases the critical temperature and makes the magnetic moment harder to form in the case of without external field. Furthermore, the increase of b will result in extending the period of the external magnetic field.

Noncommutative effects of spacetime on holographic superconductors

The Sturm-Liouville eigenvalue method is employed to analytically investigate the properties of holographic superconductors in higher dimensions in the framework of Born-Infeld electrodynamics incorporating the effects of noncommutative spacetime. In the background of pure Einstein gravity in noncommutative spacetime, we obtain the relation between the critical temperature and the charge density. We also obtain the value of the condensation operator and the critical exponent. Our findings suggest that higher the value of noncommutative parameter and Born-Infeld parameter make the condensate harder to form. We also observe that the critical temperature depends on the mass of the black hole and higher value of black hole mass is favourable for the formation of the condensate.

Massive charged BTZ black holes in asymptotically (a)dS spacetimes

Motivated by recent developments of BTZ black holes and interesting results of massive gravity, we investigate massive BTZ black holes in the presence of Maxwell and Born-Infeld (BI) electrodynamics. We study geometrical properties such as type of singularity and asymptotical behavior as well as thermodynamic structure of the solutions through canonical ensemble. We show that despite the existence of massive term, obtained solutions are asymptotically (a)dS and have a curvature singularity at the origin. Then, we regard varying cosmological constant and examine the Van der Waals like behavior of the solutions in extended phase space. In addition, we employ geometrical thermodynamic approaches and show that using Weinhold, Ruppeiner and Quevedo metrics leads to existence of ensemble dependency while HPEM metric yields consistent picture. For neutral solutions, it will be shown that generalization to massive gravity leads to the presence of non-zero temperature and heat capacity for vanishing horizon radius. Such behavior is not observed for linearly charged solutions while generalization to nonlinearly one recovers this property.

Higher dimensional holographic superconductors in Born–Infeld electrodynamics with back-reaction

In this paper, we analytically investigate the properties of holographic superconductors in higher dimensions in the framework of Born-Infeld electrodynamics taking into account the backreaction of the spacetime using the Sturm-Liouville eigenvalue method. In the background of pure Einstein and Gauss-Bonnet gravity, based on a perturbative approach, we obtain the relation between the critical temperature and the charge density. Higher value of the backreaction and Born-Infeld parameters result in a harder condensation to form in both cases. The analytical results are found to agree with the existing numerical results. We also derive an expression for the condensation operator in $d$-dimensions which yields the critical exponent to be $1/2$.

Parallel-plate and spherical capacitors in Born-Infeld electrostatics: An analytical study

In 1934, Max Born and Leopold Infeld suggested and developed a nonlinear modification of Maxwell electrodynamics, in which the electrostatic self-energy of an electron was a finite value. In this paper, after a brief introduction to Lagrangian formulation of Born-Infeld electrodynamics with an external source, the explicit forms of Gauss's law and the electrostatic energy density in Born-Infeld theory are obtained. The capacitance and the stored electrostatic energy for a parallel-plate and spherical capacitors are computed in the framework of Born-Infeld electrostatics. We show that the usual relations $U=\frac{1}{2}C_{_{\textrm{Maxwell}}}(\triangle \phi)^{2}$ and $U=\frac{q^{2}}{2C_{_{\textrm{Maxwell}}}}$ are not valid for a capacitor in Born-Infeld electrostatics. Numerical estimations in this research show that the nonlinear corrections to the capacitance and the stored electrostatic energy for a capacitor in Born-Infeld electrostatics are considerable when the potential difference between the plates of a capacitor is very large.

Approximated solutions to Born-Infeld dynamics

The Born-Infeld equation in the plane is usefully captured in complex language. The general exact solution can be written as a combination of holomorphic and anti-holomorphic functions. However, this solution only expresses the potential in an implicit way. We rework the formulation to obtain the complex potential in an explicit way, by means of a perturbative procedure. We take care of the secular behavior common to this kind of approach, by resorting to a symmetry the equation has at the considered order of approximation. We apply the method to build approximated solutions to Born-Infeld electrodynamics. We solve for BI electromagnetic waves traveling in opposite directions. We study the propagation at interfaces, with the aim of searching for effects susceptible to experimental detection. In particular, we show that a reflected wave is produced when a wave is incident on a semi-space containing a magnetostatic field.

Analytical study of holographic superconductor in Born–Infeld electrodynamics with backreaction

We generalize the analytical investigation on the properties of $s$-wave holographic superconductors in the presence of Born-Infeld nonlinear electrodynamics by taking the backreaction into account. We find that in the presence of nonlinear gauge field, one can still employ the analytical method when the backreaction is turned on. Our calculation is based on the Sturm-Liouville eigenvalue problem, which is a variational method. For the system under consideration, we obtain the relation between the critical temperature and the charge density. We find that both backreaction and Born-Infeld parameters decrease the critical temperature of the superconductor and make the condensation harder. At the ned of paper, we calculate the critical exponent associated with the condensation near the critical temperature and find that it has the universal value $1/2$ of the mean field theory.

Shock wave polarizations and optical metrics in the Born and the Born–Infeld electrodynamics

We analyze the behavior of shock waves in nonlinear theories of electrodynamics. For this, by use of generalized Hadamard step functions of increasing order, the electromagnetic potential is developed in a series expansion near the shock wave front. This brings about a corresponding expansion of the respective electromagnetic field equations which allows for deriving relations that determine the jump coefficients in the expansion series of the potential. We compute the components of a suitable gauge-normalized version of the jump coefficients given for a prescribed tetrad compatible with the shock front foliation. The solution of the first-order jump relations shows that, in contrast to linear Maxwell’s electrodynamics, in general the propagation of shock waves in nonlinear theories is governed by optical metrics and polarization conditions describing the propagation of two differently polarized waves (leading to a possible appearance of birefringence). In detail, shock waves are analyzed in the Born and Born–Infeld theories verifying that the Born–Infeld model exhibits no birefringence and the Born model does. The obtained results are compared to those ones found in literature. New results for the polarization of the two different waves are derived for Born-type electrodynamics.

Einstein-Born-Infeld-massive gravity: adS-black hole solutions and their thermodynamical properties

In this paper, we study massive gravity in the presence of Born-Infeld nonlinear electrodynamics. First, we obtain metric function related to this gravity and investigate the geometry of the solutions and find that there is an essential singularity at the origin ($r=0$). It will be shown that due to contribution of the massive part, the number, types and places of horizons may be changed. Next, we calculate the conserved and thermodynamic quantities and check the validation of the first law of thermodynamics. We also investigate thermal stability of these black holes in context of canonical ensemble. It will be shown that number, type and place of phase transition points are functions of different parameters which lead to dependency of stability conditions to these parameters. Also, it will be shown how the behavior of temperature is modified due to extension of massive gravity and strong nonlinearity parameter. Next, critical behavior of the system in extended phase space by considering cosmological constant as pressure is investigated. A study regarding neutral Einstein-massive gravity in context of extended phase space is done. Geometrical approach is employed to study the thermodynamical behavior of the system in context of heat capacity and extended phase space. It will be shown that GTs, heat capacity and extended phase space have consistent results. Finally, critical behavior of the system is investigated through use of another method. It will be pointed out that the results of this method is in agreement with other methods and follow the concepts of ordinary thermodynamics.

Extremal Einstein–Born–Infeld black holes in dilaton gravity

Motivated by considerable interests of Myers–Perry black holes, we employ the perturbative method to obtain a family of extremal charged rotating black hole solutions in odd dimensional Einstein–Born–Infeld-dilaton gravity. We start with an extremal Myers–Perry black hole with equal angular momenta, and then by adding the dilaton field and the nonlinear Born–Infeld electrodynamics, we find an extremal nonlinearly charged rotating black holes. The perturbative parameter is assumed to be the electric charge q and the perturbations are performed up to the third order. We then study the physical properties of these Born–Infeld-dilaton black holes. In particular, we show that the perturbative parameter, q, the dilaton coupling constant, α, and the Born–Infeld parameter, β, modify the Smarr formula and the values of the gyromagnetic ratio of the extremal charged rotating black holes.

Born-Infeld gravity coupled to Born-Infeld electrodynamics

We investigate spherically symmetric, static spacetimes in Eddington-inspired Born-Infeld gravity coupled to Born-Infeld electrodynamics. The two constants, $b^2$ and $\kappa$ which parametrise the Born-Infeld structures in the electrodynamics (matter) and gravity sectors, characterise the features of our analytical solutions. Black holes or naked singularities are found to arise, depending on the values of $b^2$ and $\kappa$, as well as charge and mass. Several such solutions are classified and understood through the analysis of the associated metric functions for fixed $\kappa$, varying $b^2$ and vice-versa. Further, we also compare the new metric functions with those for the known $b^2\rightarrow \infty$ (Maxwell) and the $\kappa \rightarrow 0$ (geonic black hole) cases. Interestingly, for a particular relation between these two parameters, $b^2=1/{4\kappa},\, \kappa >0$, we obtain a solution resembling the well-known Reissner-Nordstr\" om line element, albeit some modifications. Using this particular solution as the background spacetime, we study null geodesics for Born-Infeld photons and also, gravitational lensing. Among interesting features we note $(i)$ an increase in the radius of the photon sphere with increasing $\kappa$ and $(ii)$ a net positive contribution in the leading order correction term involving $\kappa$, in the weak lensing formula for the deflection angle. We also investigate the effective potential and light propagation for various other solutions through numerics and plots. In summary, our work is the first attempt towards figuring out how Born-Infeld structures in both the matter and gravity sectors can influence the nature and character of resulting gravitational fields.

Metric Relativity and the Dynamical Bridge: Highlights of Riemannian Geometry in Physics

We present an overview of recent developments concerning modifications of the geometry of space-time to describe various physical processes of interactions among classical and quantum configurations. We concentrate in two main lines of research: the Metric Relativity and the Dynamical Bridge. We describe the notion of equivalent (dragged) metric $ \widehat {g}_{\mu \nu }$ which is responsible to map the path of any accelerated body in Minkowski space-time onto a geodesic motion in such associated $\widehat {g}$ geometry. Only recently, the method introduced by Einstein in general relativity was used beyond the domain of gravitational forces to map arbitrary accelerated bodies submitted to non-Newtonian attractions onto geodesics of a modified geometry. This process has its roots in the very ancient idea to treat any dynamical problem in Classical Mechanics as nothing but a problem of static where all forces acting on a body annihilates themselves including the inertial ones. This general procedure, that concerns arbitrary forces—beyond the uses of General Relativity that is limited only to gravitational processes—is nothing but the relativistic version of the d’Alembert method in classical mechanics and consists in the principle of Metric Relativity. The main difference between gravitational interaction and all other forces concerns the universality of gravity which added to the interpretation of the equivalence principle allows all associated geometries—one for each different body in the case of non-gravitational forces—to be unified into a unique Riemannian space-time structure. The same geometrical description appears for electromagnetic waves in the optical limit within the context of nonlinear theories or material medium. Once it is largely discussed in the literature, the so-called analogue models of gravity, we will dedicate few sections on this emphasizing their relation with the new concepts introduced here. Then, we pass to the description of the Dynamical Bridge formalism which states the dynamic equivalence of nonlinear theories (driven by arbitrary scalar, spinor or vector fields) that occur in Minkowski background to theories described in associated curved geometries generated by each one of these fields. We shall see that it is possible to map the dynamical properties of a theory, say Maxwell electrodynamics in Minkowski space-time, into Born-Infeld electrodynamics described in a curved space-time the metric of which is defined in terms of the electromagnetic field itself in such way that it yields the same dynamics. It is clear that when considered in whatever unique geometrical structure, these two theories are not the same; they do not describe the same phenomenon. However, we shall see that by a convenient modification of the metric of space-time, an equivalence appears that establishes a bridge between these two theories making they represent the same phenomenon. This method was recently used to achieve a successful geometric scalar theory of gravity. At the end, we briefly review the proposal of geometrization of quantum mechanics in the de Broglie-Bohm formulation using an enlarged non-Riemannian (Weyl) structure.

On analytical study of holographic superconductors with Born–Infeld electrodynamics

Based on the Sturm–Liouville eigenvalue problem, Banerjee et al. proposed a perturbative approach to analytically investigate the properties of the (2+1)-dimensional superconductor with Born–Infeld electrodynamics (Banerjee et al., 2013) [29]. By introducing an iterative procedure, we will further improve the analytical results and the consistency with the numerical findings, and can easily extend the analytical study to the higher-dimensional superconductor with Born–Infeld electrodynamics. We observe that the higher Born–Infeld corrections make it harder for the condensation to form but do not affect the critical phenomena of the system. Our analytical results can be used to back up the numerical computations for the holographic superconductors with various condensates in Born–Infeld electrodynamics.

Born–Infeld electrodynamics in very special relativity

In this work we discuss the properties of a modified Born–Infeld electrodynamics in the framework of very special relativity (VSR). This proposal allows us to study VSR mass effects in a gauge-invariant context of nonlinear electrodynamics. It is analyzed in detail the electrostatic solutions for two different cases, as well as the VSR dispersion relations are found to be of a massive particle with nonlinear modifications. Afterwards, the field energy and static potential are computed, in the latter we find from the VSR contribution a novel long-range 1/L3 correction to the Coulomb potential, in contrast to the 1/L5 correction of the usual Born–Infeld theory.

Thermodynamics of third-order Lovelock-AdS black holes in the presence of Born-Infeld type nonlinear electrodynamics

In this paper, we obtain topological black hole solutions of third-order Lovelock gravity coupled with two classes of Born-Infeld-type nonlinear electrodynamics with anti--de Sitter asymptotic structure. We investigate geometric and thermodynamics properties of the solutions and obtain conserved quantities of the black holes. We examine the first law of thermodynamics and find that the conserved and thermodynamic quantities of the black hole solutions satisfy the first law of thermodynamics. Finally, we calculate the heat capacity and determinant of the Hessian matrix to evaluate thermal stability in both canonical and grand canonical ensembles. Moreover, we consider the extended phase space thermodynamics to obtain a generalized first law of thermodynamics as well as the extended Smarr formula.

Holographic thermalization with a chemical potential from Born-Infeld electrodynamics

The problem of holographic thermalization in the framework of Einstein gravity coupled to Born-Infeld nonlinear electrodynamics is investigated. We use equal time two-point correlation functions and expectation values of Wilson loop operators in the boundary quantum field theory as probes of thermalization, which have dual gravity descriptions in terms of geodesic lengths and minimal area surfaces in the bulk spacetime. The full range of values of the chemical potential per temperature ratio μ/T on the boundary is explored. The numerical results show that the effect of the charge on the thermalization time is similar to the one obtained with Maxwell electrodynamics, namely the larger the charge the later thermalization occurs. The Born-Infeld parameter, on the other hand, has the opposite effect: the more nonlinear the theory is, the sooner it thermalizes. We also study the thermalization velocity and how the parameters affect the phase transition point separating the thermalization process into an accelerating phase and a decelerating phase.

Analytical Calculation of Stored Electrostatic Energy per Unit Length for an Infinite Charged Line and an Infinitely Long Cylinder in the Framework of Born-Infeld Electrostatics

More than 80 years ago, Born-Infeld electrodynamics was proposed in order to remove the point charge singularity in Maxwell electrodynamics. In this work, after a brief introduction to Lagrangian formulation of Abelian Born-Infeld model in the presence of an external source, we obtain the explicit forms of Gauss’s law and the energy density of an electrostatic field for Born-Infeld electrostatics. The electric field and the stored electrostatic energy per unit length for an infinite charged line and an infinitely long cylinder in Born-Infeld electrostatics are calculated. Numerical estimations in this paper show that the nonlinear corrections to Maxwell electrodynamics are considerable only for strong electric fields. We present an action functional for Abelian Born-Infeld model with an auxiliary scalar field in the presence of an external source. This action functional is a generalization of the action functional which was presented by Tseytlin in his studies on low energy dynamics ofD-branes (Nucl. Phys. B469, 51 (1996); Int. J. Mod. Phys. A 19, 3427 (2004)). Finally, we derive the symmetric energy-momentum tensor for Abelian Born-Infeld model with an auxiliary scalar field.

On the NUT–Born–Infeld-[formula omitted] spacetime

The stationary axisymmetric spacetime coupled to nonlinear Born–Infeld electrodynamics is studied; the solution was derived by Plebański et al. (1984) in terms of integrals. It is characterized by six free parameters: mass, NUT charge, electric and magnetic charge, Born–Infeld parameter and cosmological constant. The geodesic and Lorentz force equations are integrated on the equatorial plane, and the effect of varying the parameters in the effective potential is analyzed. The trajectories of light and those for charged particles are discussed as well. Finally the conditions for the extreme black hole are determined, obtaining bounds between the charges, the Born–Infeld parameter and the cosmological constant.

Comment on “Extended Born-Infeld theory and the bouncing magnetic universe”

In a recent paper [Phys. Rev. D{\bf 85}, 023528 (2012)] the authors proposed a generalized Born-Infeld electrodynamics coupled to general relativity which produces a nonsingular bouncing universe. For a magnetic universe the resulting cosmic evolution inevitably interpolates between asymptotic de Sitter states. Here we shall show that (i) the above theory does not have the standard weak field Maxwell limit, (ii) a sudden curvature singularity -- not better than the big bang -- arises, (iii) the speed of sound squared is a negative quantity signaling instability against small perturbations of the background energy density, and that (iv) the conclusion about the inevitability of the asymptotic vacuum regime in a magnetic universe is wrong.