Super-entropic black holes possess finite-area but noncompact event horizons and violate the reverse isoperimetric inequality. It has been conjectured that such black holes always have negative specific heat at constant volume $C_{V}$ or negative specific heat at constant pressure $C_{P}$ whenever $C_{V}>0$, making them unstable in extended thermodynamics. In this paper, we test this instability conjecture on a family of nonlinear electrodynamics black holes, namely $3$D Einstein-Born-Infeld (EBI) AdS black holes. Our results show that when nonlinear electrodynamics effects are weak, the instability conjecture is valid. However, the conjecture can be violated in some parameter region when nonlinear electrodynamics effects are strong enough. This observation thus provides a counter example to the instability conjecture, which suggests that super-entropic black holes could be thermodynamically stable.
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 $r=0$.
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.
In this work, we take a short recap of a formal framework of the Eddington-inspired Born-Infeld (EiBI) theory of gravity and derive the point-like Lagrangian for underlying theory based on the use of Noether gauge symmetries (NGS). We study a Hessian matrix and quantify Euler-Lagrange equations of EiBI universe. We discuss the NGS approach for the Eddington-inspired Born-Infeld theory and show that there exists the de Sitter solution in this gravity model.
We review a recent proposal to describe dark matter and dark energy based on an Eddington-Born-Infeld action. The theory is successful in describing the evolution of the expansion factor as well as galactic flat rotation curves. Fluctuations and the CMB spectra are currently under study. This paper in written in honor of Claudio Bunster on the occasion of his sixtieth birthday.
A class of perturbative charged rotating dilaton black hole solutions coupled to the nonlinear Born-Infeld electrodynamics is presented. The strategy for obtaining these solutions is to start from Myers-Perry solutions, and then considering the effects of the dilaton field, Born-Infeld parameter as well as the electric charge as a perturbative parameter. We perform the perturbations up to 4th order in the extremal black holes of Einstein-Born-Infeld-dilaton gravity with equal angular momentum and arbitrary dilaton coupling constant. We discuss the physical properties of these black holes and s…
The stationary axisymmetric spacetime coupled to nonlinear Born-Infeld electrodynamics is studied. The solution was derived by Plebanski et al (1984) and 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, and a qualitative analysis of the effect of varying the parameters in the effective potential is provided. Then the light and charged particle trajectories are discussed. The conditions that determine an extreme black hole are presented as well.
Born-Infeld deformation strategy to smooth theories having divergent solutions is applied to the teleparallel equivalent of General Relativity. The equivalence between teleparallelism and General Relativity is exploited to obtain a deformed theory of gravity based on second order differential equations, since teleparallel Lagrangian is built just from first derivatives of the vierbein. We show that Born-Infeld teleparallelism cures the initial singularity in a spatially flat FRW universe; moreover, it provides a natural inflationary stage without resorting to an inflaton field. The Born-Infeld…
We show that all thermodynamic quantities of the Einstein-Born-Infeld black holes in three dimensions can be obtained from the dilaton and its potential of two dimensional dilaton gravity through the dimensional reduction. These are all between non-rotating uncharged BTZ black hole (NBTZ) and charged BTZ black hole (CBTZ).
Employing higher order perturbation theory, we find a new class of perturbative extremal rotating black hole solutions with Born-Infeld electric charge in odd D-dimensional spacetime. The seed solution is an odd dimensional extremal Myers-Perry black hole with equal angular momenta to which a perturbative nonlinear electric Born-Infeld field charge q is added maintaining the extremality condition. The perturbations are performed up to third order. We also study some physical properties of these black holes. In particular, it is shown that the values of the gyromagnetic ratio of the black holes…
In this paper, quartic quasi-topological black holes in the presence of a nonlinear electromagnetic Born-Infeld field is presented. By using the metric parameters, the charged black hole solutions of quasi-topological Born-Infeld gravity is considered. The thermodynamics of these black holes are investigated and I show that the thermodynamics and conserved quantities verify the first law of thermodynamics. I also introduce the thermodynamics of asymptotically AdS rotating black branes with flat horizon of these class of solutions and I calculate the finite action by use of the counterterm meth…
A new solution of the Einstein-Born-Infeld theory in 2+1 space-time is derived. A new solution has no horizon there are two singularity. This space-time has two singular points, however, one of the point at the origin is not in the physical region. We also investigate the energycondition. Then, weak energy condition is satisfied. However, causal energy condition is violated.
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 investigate the horizon structure of the rotating Einstein-Born-Infeld solution which goes over to the Einstein-Maxwell's Kerr-Newman solution as the Born-Infeld parameter goes to infinity ($β\rightarrow \infty$). We find that for a given $β$, mass $M$ and charge $Q$, there exist critical spinning parameter $a_{E}$ and $r_{H}^{E}$, which corresponds to an extremal Einstein-Born-Infeld black hole with degenerate horizons, and $a_{E}$ decreases and $r_{H}^{E}$ increases with increase in the Born-Infeld parameter $β$. While $a<a_{E}$ describe a non-extremal Einstein-Born-Infeld black hole with…
This paper studies the self-similar singularity phenomenon of zero mean curvature equation including Born-Infeld equation, space-like surfaces with vanishing mean curvature equation and membrane equation which arises in string theory and geometric minimal surfaces theory. We show that there exist new explicit self-similar solutions for Born-Infeld equation, space-like surfaces with vanishing mean curvature equation and membrane equation in Minkowski space $R^{1+3}$ with respect to the radially symmetric case.
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.
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 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 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 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.
It has been shown that the Strong Cosmic Censorship (SCC) can be violated by a scalar field in a near-extremal Reissner-Nordstrom-de Sitter black hole. In this paper, we investigate the Strong Cosmic Censorship in a Born-Infeld-de Sitter black hole by a scalar perturbation field with/without a charge. When the Born-Infeld parameter b becomes small, the nonlinear electrodynamics effect starts to play an important role and tends to rescue SCC. Specifically, we find that the SCC violation region decreases in size with decreasing b. Moreover, for a sufficiently small b, SCC can always be restored …
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.
