Using the Teleparallel Equivalent of General Relativity formulated in Weitzenböck spacetime, we thoroughly explore a kind of Born-Infeld regular gravity leading to second order field equations for the vielbein components. We explicitly solve the equations of motion for two examples: the extended BTZ black hole, which results to exist even if the cosmological constant is positive, and a cosmological model with matter, where the scale factor results to be well behaved, giving so a singularity-free solution.
The Born-Infeld theory of the gravitational field formulated in Weitzenbock spacetime is studied in detail. The action, constructed quadratically upon the torsion two-form, reduces to Einstein gravity in the low field limit where the Born-Infeld constant goes to infinity, and it is described by second order field equations for the vielbein field in $D$ spacetime dimensions. The equations of motion are derived, and a number of properties coming from them are discussed. In particular, we show that under fairly general circumstances, the equations of motion are those of Einstein's General Relativ…
We study the effects of the Born-Infeld electrodynamics on the holographic superconductors in the background of a Schwarzschild AdS black hole spacetime. We find that the presence of Born-Infeld scale parameter decreases the critical temperature and the ratio of the gap frequency in conductivity to the critical temperature for the condensates. Our results means that it is harder for the scalar condensation to form in the Born-Infeld electrodynamics.
We present some obvious physical requirements on gravitational avatars of non-linear electrodynamics and illustrate them with explicit determinantal Born-Infeld-Einstein models. A related procedure, using compensating Weyl scalars, permits us to formulate conformally invariant versions of these systems as well.
We investigate the flux compactification mechanism in simple toy models of Einstein-Born-Infeld theories. These are the direct generalizations of the Einstein-Maxwell flux compactifications that recently gained fame as a toy model for tunneling in the landscape. Our investigation reveals that the Born-Infeld form does not significantly modify the qualitative result of the Einstein-Maxwell theory. for the case of Einstein-Higgs theory, however, we found that the effect of Born-Infeld nonlinearity is to render all q>1 extradimensional compactification unstable against semiclassical tunneling to …
The topological classification of critical points of black holes in 4D Einstein-Gauss-Bonnet gravity coupled to Born-Infeld theory is investigated. Considered independently, Born-infeld corrections to the Einstein action alter the topological charge of critical points of the charged AdS black hole system, whereas the Gauss-Bonnet corrections do not. For the combined system though, the total topological charge of the Einstein-Gauss-Bonnet theory is unaltered in the presence of Born-Infeld coupling.
We consider Einstein Born-Infeld theory with a null fluid in Kerr-Schild Geometry. We find accelerated charge solutions of this theory. Our solutions reduce to the Plebanski solution when the acceleration vanishes and to the Bonnor-Vaidya solution as the Born-Infeld parameter b goes to infinity. We also give the explicit form of the energy flux formula due to the acceleration of the charged sources.
We study static spherically symmetric monopole solutions in non-Abelian Einstein-Born-Infeld-Higgs model with normal trace structure. These monopoles are similar to the corresponding solution with symmetrised trace structure and are existing only up to some critical value of the strength of the gravitational interaction. In addition, similar to their flat space counterpart, they also admit a critical value of the Born-Infeld parameter $\b$.
Properties of the Dirac-Born-Infeld Lagrangian analogous to those of the Nambu-Goto String are analysed. In particular the Lagrangian is shown to be constant or zero on the space of solutions of the equations of motion if the Lagrangian is taken to any power other than 1/2.
In this paper, we analytically investigate the effect of adding an external magnetic field in presence of Born-Infeld corrections to a holographic superconductor in the probe limit. The technique employed is based on the matching of the solutions to the field equations near the horizon and the asymptotic AdS region. We obtain expressions for the critical temperature and the condensation values explicitly to all orders in the Born-Infeld parameter. The value of the critical magnetic field is finally obtained and is found to get affected by the Born-Infeld parameter.
We study a new approach for the wormhole construction in Einstein-Born-Infeld gravity, which does not require exotic matters in the Einstein equation. The Born-Infeld field equation is not modified from "coordinate independent" conditions of continuous metric tensor and its derivatives, even though the Born-Infeld fields have discontinuities in their derivatives at the throat in general. We study the relation of the newly introduced conditions with the usual continuity equation for the energy-momentum tensor and the gravitational Bianchi identity. We find that there is no violation of energy c…
By using a novel technique that establishes a correspondence between general relativity and metric-affine theories based on the Ricci tensor, we are able to set stringent constraints on the free parameter of Born-Infeld gravity from the ones recently obtained for Born-Infeld electrodynamics by using light-by-light scattering data from ATLAS. We also discuss how these gravity theories plus matter fit within an effective field theory framework.
We investigate black hole solutions in the Einstein-Born-Infeld system. We clarify the role played by derivative corrections to the Born-Infeld (BI) action. The qulitative differences from the case without derivative corrections are: (i) there is no particlelike solution. (ii) the existence of the inner horizon is restricted to the near extreme solutions. (iii) contribution of the BI parameter $b$ to the gravitational mass and the Hawking temperature works in the opposite direction.
We study the quasinormal mode of the perturbation of the scalar field interacting with the electromagnetic field in the backgrounds of Schwarzschild AdS black hole, the Reissner-Nordstrom AdS black hole and the Born-Infeld AdS black hole. We disclose influence by the electric charge $Q$, the coupling between the scalar and electromagnetic field $q$ and the Born-Infeld parameter $b$ on the quasinormal frequencies of the scalar perturbation. We observe the possible growing mode in the perturbation when the scalar field strongly couples to the electromagnetic field. When the electromagnetic field…
We study the thermodynamics of $D$-dimensional Born-Infeld AdS black holes in the extended phase space. We find that the usual small-large black hole phase transition, which exhibits analogy with the Van de Waals liquid-gas system holds in all dimensions greater than three. However, different from the four-dimensional case, in the system of higher dimensional Born-Infeld AdS black holes there is no reentrant phase transition. For the three-dimensional Born-Infeld AS black hole, there does not exist critical phenomena.
Based on the Sturm-Liouville eigenvalue problem, Banerjee \emph{et al.} proposed a perturbative approach to analytically investigate the properties of the ($2+1$)-dimensional superconductor with Born-Infeld electrodynamics [Phys. Rev. D {\bf 87}, 104001 (2013)]. 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 condensati…
We find multicenter (Majumdar-Papapetrou type) solutions of Eddington-inspired Born-Infeld gravity coupled to electromagnetic fields governed by a Born-Infeld-like Lagrangian. We construct the general solution for an arbitrary number of centers in equilibrium and then discuss the properties of their one-particle configurations, including the existence of bounces and the regularity (geodesic completeness) of these spacetimes. Our method can be used to construct multicenter solutions in other theories of gravity.
We analytically study the holographic superconductors for Born-Infeld electrodynamics in Gauss-Bonnet gravity with backreactions. We note that the analytic method is still powerful for this complex system and the results obtained by the analytical and numerical computations are consistent. We find that the critical temperature decreases with the increase of the backreactions, Gauss-Bonnet, and Born-Infeld parameters, which means that increase of the strength of these effects will make the scalar hair harder to form. Furthermore, the Gauss-Bonnet factor modifies the critical temperature more si…
We encode dynamical symmetries of Born-Infeld theory in a geometry on the tangent bundle of generally curved spacetime manifolds. The resulting covariant formulation of a maximal acceleration extension of special and general relativity is put to use in the discussion of particular point particle dynamics and the transition to a first quantized theory.
We investigate spherically symmetric, static spacetimes in Eddington-inspired Born-Infeld gravity coupled to Born-Infeld electrodynamics. The two constants, $b^2$ and $κ$ 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 $κ$, as well as charge and mass. Several such solutions are classified and understood through the analysis of the associated metric functions for fixed $κ$, varying $b^2$ and vice-vers…
Spherically symmetric thin-shell wormholes are studied within the framework of Einstein-Born-Infeld theory. We analyze the exotic matter content and find that for certain values of the Born-Infeld parameter the amount of exotic matter on the shell can be reduced in relation to the Maxwell case. We also examine the mechanical stability of the wormhole configurations under radial perturbations preserving the spherical symmetry.
We find static spherically symmetric monopoles in Einstein-Born-Infeld-Higgs model in 3+1 dimensions. The solutions exist only when a parameter $\a $ (related to the strength of Gravitational interaction) does not exceed certain critical value. We also discuss magnetically charged non Abelian black holes in this model. We analyse these solutions numerically.
We define various Born-Infeld gravity theories in 3+1 dimensions which reduce to Horava's model at the quadratic level in small curvature expansion. In their exact forms, our actions provide z->(infinity) extensions of Horava's gravity, but when small curvature expansion is used, they reproduce finite z models, including some half-integer ones.
We investigate the holographic entanglement entropy in the insulator/superconductor phase transition for the Born-Infeld electrodynamics with full backreaction in five-dimensional AdS soliton spacetime. We note that the holographic entanglement entropy is a good probe to study the properties of the phase transition, and the Born-Infeld factor $b$ has no effect on the critical chemical potential $μ_c$. We find that both in the half space and the belt one, the non-monotonic behavior of the entanglement entropy versus the chemical potential is a general property, and the entanglement entropy incr…
We here explore black holes in the third order Lovelock gravity coupling with nonlinear Born-Infeld electromagnetic field. Considering special second and third order coefficients ($\hatα_2^2=3\hatα_3=α^2$), we analyze the thermodynamics of third order Lovelock-Born-Infeld black holes and, in 7-dimensional AdS space-time, discuss the stability of black holes in different event horizon structures. We find that the cosmological constant $Λ$ plays an important role in the distribution of stable regions of black holes.
We derive exact magnetically charged, static and spherically symmetric black hole solutions of the four-dimensional Einstein-Born-Infeld-dilaton gravity. These solutions are neither asymptotically flat nor (anti)-de Sitter. The properties of the solutions are discussed. It is shown that the black holes are stable against linear radial perturbations.
In this paper, based on the Sturm-Liouville eigenvalue problem, we analytically investigate several properties of holographic s-wave superconductors in the background of a Schwarzschild-AdS spacetime in the framework of Born-Infeld electrodynamics. Based on a perturbative approach, we explicitly find the relation between the critical temperature and the charge density and also the fact that the Born-Infeld coupling parameter indeed affects the formation of scalar hair at low temperatures. Higher value of the Born-Infeld parameter results in a harder condensation to form. We further compute the…
Dynamical symmetries of Born-Infeld theory associated with its maximal field strength are encoded in a geometry on the tangent bundle of spacetime manifolds. The resulting extension of general relativity respecting a finite upper bound on accelerations is put to use in the discussion of particle dynamics, first quantization, and the derivation of a correction to the Thomas precession.
We construct regular and black hole solutions in SU(2) Einstein-Born-Infeld theory. These solutions have many features in common with the corresponding SU(2) Einstein-Yang-Mills solutions. In particular, sequences of neutral non-abelian solutions tend to magnetically charged limiting solutions, related to embedded abelian solutions. Thermodynamic properties of the black hole solutions are addressed.
In this paper we investigate the perturbations by a massless Dirac spinor of a Born-Infeld black hole. The decay rates of the spinor field which is given by the quasinormal mode frequencies are computed using the sixth order WKB approximation. The behavior of the quasi normal modes with the non-linear parameter, temperature and charge of the black hole are analyzed in detail. We also compare the decay rates of the Born-Infeld black hole with its linear counter-part Reissner-Nordstrom black hole.
We construct a new class of perturbative extremal charged rotating black hole solutions in five dimensions in the Einstein--Born-Infeld theory. We start with an extremal five-dimensional Myers-Perry black hole seed in which the two possible angular momenta have equal magnitude, and add Born-Infeld electrical charge keeping the extremality condition as a constraint. The perturbative parameter is assumed to be the electric charge $q$ and the perturbations are performed up to 4th order. We also study some physical properties of these black holes. It is shown that the perturbative parameter $q$ an…
We study the Einstein-Born-Infeld (EBI) theory where the hairy black hole was found as the EBI black hole by using Hod's idea. The hair extends beyond the photon-sphere of the EBI black hole spacetimes. We show that the region beyond the photon-sphere involves more than half of the total hair's mass, which respects Hod's conjectured bound.
Cosmology in Eddington-inspired Born-Infeld gravity is investigated using a scalar Born-Infeld field (e.g. tachyon condensate) as matter. In this way, both in the gravity and matter sectors we have Born-Infeld-like structures characterized by their actions and via two separate constants, $κ$ and $α_T^2$ respectively. With a particular choice of the form of $\dotϕ$ (the time derivative of the Born-Infeld scalar), analytical cosmological solutions are found. Thereafter, we explore some of the unique features of the corresponding cosmological spacetimes. For $κ>0$, our solution has a de Sitter-li…
We argue that Einstein gravity coupled to a Born-Infeld theory provides an attractive candidate to represent dark matter and dark energy. For cosmological models, the Born-Infeld field has an equation of state which interpolates between matter, w=0 (small times), and a cosmological constant w=-1 (large times). On galactic scales, the Born-Infeld field predicts asymptotically flat rotation curves.
We investigate, in the probe limit, the negative refraction in the generalized superconductors with the Born-Infeld electrodynamics. We observe that the system has a negative Depine-Lakhtakia index in the superconducting phase at small frequencies and the greater the Born-Infeld corrections the larger the range of frequencies or the range of temperatures for which the negative refraction occurs. Furthermore, we find that the tunable Born-Infeld parameter can be used to improve the propagation of light in the holographic setup. Our analysis indicates that the Born-Infeld electrodynamics plays a…
We investigate the holographic superconductors in Gauss-Bonnet gravity with Born-Infeld electrodynamics. We find that the Gauss-Bonnet constant, the model parameters and the Born-Infeld coupling parameter will affect the formation of the scalar hair, the transition point of the phase transition from the second order to the first order, and the relation connecting the gap frequency in conductivity with the critical temperature. The combination of the Gauss-Bonnet gravity and the Born-Infeld electrodynamics provides richer physics in the phase transition and the condensation of the scalar hair.
We show exact solutions of Born-Infeld theory for electromagnetic plane waves propagating in the presence of static background fields. The non-linear character of Born-Infeld equations generates an interaction between background and wave that changes the speed of propagation and adds a longitudinal component to the wave. As a consequence, in a magnetic background the ray direction differs from the propagation direction --a behavior resembling the one of a wave in an anisotropic medium--. This feature could open up a way to experimental tests of Born-Infeld theory.
We construct new gravitational vacuum star solutions with a Born-Infeld phantom replacing the de Sitter interior. The model allows for a wide range of masses and radii required by phenomenology, and can be motivated from low energy string theory.
We discuss the possibility that a Born-Infeld condensate coupled to neutrinos can generate both neutrino masses and an effective cosmological constant. In particular, an effective field theory is provided capable of dynamically realizing the neutrino superfluid phase firstly suggested by Ginzburg and Zharkov. In such a case, neutrinos acquire a mass gap inside the Born-Infeld ether forming a long-range Cooper pair. Phenomenological implications of the approach are also discussed.
We consider the Noether Symmetry Approach for a cosmological model derived from a tachyon scalar field $T$ with a Dirac-Born-Infeld Lagrangian and a potential $V(T)$. Furthermore, we assume a coupled canonical scalar field $ϕ$ with an arbitrary interaction potential $B(T,ϕ)$. Exact solutions are derived consistent with the accelerated behavior of cosmic fluid.
Accelerating dynamics from Born-Infeld-$f(R)$ gravity are studied in a simplified conformal approach without matter. Explicit unification of inflation with late-time acceleration is realized within this singular inflation approach, which is similar to Odintsov-Oikonomou singular $f(R)$ inflation. Our model turns out to be consistent with the latest release of Planck data.
The vacuum, static, and spherically symmetric solutions in the mimetic Born-Infeld gravity are studied. The mimetic Born-Infeld gravity is a reformulation of the Eddington-inspired-Born-Infeld (EiBI) model under the mimetic approach. Due to the mimetic field, the theory contains non-trivial vacuum solutions different from those in Einstein gravity. We find that with the existence of the mimetic field, the spacelike singularity inside a Schwarzschild black hole could be altered to a lightlike singularity, even though the curvature invariants still diverge at the singularity. Furthermore, in thi…
In this note one suggests a possibility of direct observation of the $θ$-parameter, introduced in the Born--Infeld theory of electroweak and gravitational fields, developed in quant-ph/0202024. Namely, one may treat $θ$ as a universal constant, responsible for correction to the Coulomb and Newton laws, allowing direct interaction between electrical charges and masses.
We consider two types of modifications of Born-Infeld gravity in the Palatini formulation and explore their dynamics in the early universe. One of these families considers $f(R)$ corrections to the Born-Infeld Lagrangian, which can be seen as modifications of the dynamics produced by the quantum effects of matter, while the other consists on different powers of the elementary building block of the Born-Infeld Lagrangian, which we denote by $|\hatΩ|$. We find that the two types of nonsingular solutions that arise in the original Born-Infeld theory are also present in these extensions, being bou…
Eddington-inspired Born-Infeld gravity (EiBI) gravity is a recently proposed modified theory of gravity, based on the classic work of Eddington and on Born-Infeld nonlinear electrodynamics. In this paper, we consider the possibility that wormhole geometries are sustained in EiBI gravity. We present the gravitational field equations for an anisotropic stress-energy tensor and consider the generic conditions, for the auxiliary metric, at the wormhole throat. In addition to this, we obtain an exact solution for an asymptotically flat wormhole.
Born-Infeld electromagnetic waves interacting with a static magnetic background are studied in an expanding universe. The non-linear character of Born-Infeld electrodynamics modifies the relation between the energy flux and the distance to the source, which gains a new dependence on the redshift that is governed by the background field. We compute the luminosity distance as a function of the redshift and compare with Maxwellian curves for supernovae type Ia.
We introduce new black hole solutions to the Einstein-Yang-Mills-Born-Infeld (EYMBI), Einstein-Yang-Mills-Born-Infeld-Gauss-Bonnet (EYMBIGB) and Einstein-Yang-Mills-Born-Infeld-Gauss-Bonnet-Lovelock (EYMBIGBL) gravities in higher dimensions $N\geq 5$ to investigate the roles of Born-Infeld parameter $β$. It is shown that, these solutions in the limits of $β\to 0,$ and $β\to \infty ,$ represent pure gravity and gravity coupled with Yang-Mills fields, respectively. For $0<β<\infty $ it yields a variety of black holes, supporting even regular ones at $r=0$.
We investigate the cosmological evolution of the system of a Dirac-Born-Infeld field plus a perfect fluid. We analyze the existence and stability of scaling solutions for the AdS throat and the quadratic potential. We find that the scaling solutions exist when the equation of state of the perfect fluid is negative and in the ultra-relativistic limit.
Motivated by thermodynamic analogy of black holes and Van der Waals liquid/gas system, in this paper, we study $P-V$ criticality of both dilatonic Born-Infeld black holes and their conformal solutions, Brans-Dicke-Born-Infeld solutions. Due to the conformal constraint, we have to neglect the old Lagrangian of dilatonic Born-Infeld theory and its black hole solutions, and introduce a new one. We obtain spherically symmetric nonlinearly charged black hole solutions in both Einstein and Jordan frames and then, we calculate the related conserved and thermodynamic quantities. After that, we extend …
In this work a new asymptotically flat solution of the coupled Einstein-Born-Infeld equations for a static spherically symmetric space-time is obtained. When the intrinsic mass is zero the resulting spacetime is regular everywhere, in the sense given by B. Hoffmann and L. Infeld in 1937, and the Einstein-Born-Infeld theory leads to the identification of the gravitational with the electromagnetic mass.
In this work we study the trajectories of test particles in a geometry that is the nonlinear electromagnetic generalization of the Reissner-Nordstrom solution. The studied spacetime is a Einstein-Born-Infeld solution, nonsingular outside a regular event horizon and characterized by three parameters: mass $M$, charge $Q$ and the Born-Infeld parameter $b$ related to the magnitude of the electric field at the origin. Asymptotically it is a Reissner-Nordstrom solution
We construct spherically symmetric thin-shell wormholes supported by a generalized Chaplygin gas in Born-Infeld electrodynamics coupled to Einstein gravity, and we analyze their stability under radial perturbations. For different values of the Born-Infeld parameter and the charge, we compare the results with those obtained in a previous work for Maxwell electrodynamics. The stability region in the parameter space reduces and then disappears as the value of the Born-Infeld parameter is modified in the sense of a larger departure from Maxwell theory.
The three-dimensional static and circularly symmetric solution of the Einstein-Born-Infeld-dilaton system is derived. The solutions corresponding to low energy string theory are investigated in detail, which include black hole solutions if the cosmological constant is negative and the mass parameter exceeds a certain critical value. Some differences between the Born-Infeld nonlinear electrodynamics and the Maxwell electrodynamics are revealed.
Generalizations of gravitational Born-Infeld type lagrangians are investigated. Phenomenological constraints (reduction to Einstein-Hilbert action for small curvature, spin two ghost freedom and absence of Coulomb like Schwarschild singularity) select one effective lagrangian whose dynamics is dictated by the tensors g_{μν} and R_{μνρσ}(not R_{μν} or the scalar R).
In this paper I examine black hole and cosmological space-times in Born-Infeld-Einstein theory with electric and magnetic charges. The field equations are derived and written in the form $G_{μν}=-κT_{μν}$ for spherically symmetric space-times. The energy-momentum tensor is not the Born-Infeld energy-momentum tensor, but can be obtained from Born-Infeld theory by letting $a\to ia$, where $a$ is the Born-Infeld parameter. It is shown that there is a curvature singularity in spherically symmetric space-times at a nonzero radial coordinate and that, as in Reissner-Nordstrom space-times, there are …
The Ostrogradsky instability of higher derivative Lagrangians is derived from first principles using Control theory and Lyapunov Stability Analysis. This result is then used to argue that Born-Infeld Lagrangians are viable modifications of the Einstein-Hilbert action provided the action is varied in accordance with the Palatini formalism, in contrast to the metric formalism. Finally, the Born-Infeld version of the FRW equations are derived and the cosmological dynamics is studied for matter dominated closed and open universes, and the results are compared with the usual cosmology.
We demonstrated that the new N=2 Born-Infeld action with two N=1 vector supermultiplets, i.e. n=2 case considered as the example in the recent paper by S. Ferrara, M. Porrati and A. Sagnotti, is some sort of complexification of J. Bagger and A. Galperin construction of N=2 Born-Infeld action. Thus, novel features could be expected only for n>2 cases, if the standard action is considered.
