Maximo Banados
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.
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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.
Note About Born-Infeld Inspired Gravity Coupled Non-Minimally to Scalar Fields and Eddington Gravity with Matter
本文研究非最小耦合标量场的 Born-Infeld 启发引力正则结构，并构造多标量场耦合的 Eddington 引力，使其哈密顿量等价于最小耦合标量场的广义相对论。
We discuss some of the consequences of changing the matter to gravity coupling without affecting the gravitational dynamics. The Einstein tensor is usually assumed to be proportional to the stress tensor due to the divergence free property of both object. This is not the only consistent way to couple matter to gravity; we explore some aspect of consistent modification to the matter/gravity coupling using the recently proposed Eddington inspired Born Infeld extension of gravity.
We apply Kaluza's procedure to Eddington-inspired Born-Infeld action in gravity in five dimensions. The resulting action contains, in addition to the usual four-dimensional actions for gravity and electromagnetism, nonlinear couplings between the electromagnetic field strength and curvature. Considering the spherically symmetric solution as an example we find the lowest order corrections for the Reissner-Nordström metric and the electromagnetic field.
Black Holes Surrounded by Perfect Fluid Dark Matter in Eddington-inspired Born-Infeld Gravity
本文研究了在埃德蒙顿启发布林-伊尔德引力中，周围由完美流体暗物质包围的黑洞的引力场解及其稳定性特性。
The O(4)-symmetric regular instanton solutions are studied within the framework of the Eddington-inspired-Born-Infeld gravity (EiBI). We find that the behavior of the solution would deviate from that in Einstein gravity when the kinetic energy of the scalar field is sufficiently large. The tunneling probability is calculated numerically in different parameter space. We find that the tunneling probability would increase with the Born-Infeld coupling constant, which is assumed to be positive in this paper. Furthermore, we discover a neck feature in the physical instanton solutions when the kinet…
Covariant Canonical Formalism For Born-Infeld Inspired Gravity in Palatini Formulation
本文在协变正则形式框架下分析了Palatini表述的Born-Infeld启发引力，确定了其协变哈密顿量及相应的运动方程。
In this work we calculate the angular deflection of light in the strong field limit in two spacetimes which were previously studied within the Eddington-inspired Born-Infeld gravity (EiBI), namely, a black hole and a wormhole, both with topological charge. We show that the presence of the parameters characterizing EiBI and the topological charge promote significant changes in the angular deflection of light with respect to that one obtained in Schwarzschild spacetime. Using the expression for angular deflection in the strong field limit, we calculate the position and magnification of the respe…
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 $r=0$.
In this paper we modify the EiBI model to realize a varying cosmological constant which is determined by matter distribution. We find that the Newton's constant is also variable and its change is related to the change of cosmological constant. And then we study its cosmological behavior. We find that the early universe will have different behaviors if we take different forms of pending functions. And we can avoid singularity in early universe just like the original EiBI model.
In this paper we study the cosmological evolution of the universe filled with a perfect fluid in the Eddington-inspired Born-Infeld gravity. Applying an alternative method in which the evolution of the scale factor for this theory is linked to the cosmographic parameters, we obtain a dynamical dark energy solution where the singularity (through a regular bounce or a loitering phase) still can be avoided for $κ>0$ with $w>0$. For the range $-1<w<0$, the results lead us to universes that experience an unlimited rate of expansion with finite density. Also, we obtain a possible maximum value of $H…
Ideal Fluids In Born-Infeld Inspired Gravity
本文研究了受Born-Infeld启发的引力与理想流体作用功能，推导了运动方程并确定了规范形式。
We give the Buchdahl stability bound in Eddington-inspired Born-Infeld (EiBI) gravity. We show that this bound depends on an energy condition controlled by the model parameter $κ$. From this bound, we can constrain $κ\lesssim 10^{8}\text{m}^2$ if a neutron star with a mass around $3M_{\odot}$ is observed in the future. In addition, to avoid the potential pathologies in EiBI, a \emph{Hagedorn-like} equation of state associated with $κ$ at the center of a compact star is inevitable, which is similar to the Hagedorn temperature in string theory.
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.
Canonical Form of Born-Infeld Inspired Gravity Coupled to Scalar Fields
本文利用Faddeev-Jackiw方法推导Born-Infeld启发的引力与标量场耦合的正则形式，发现其正则作用量分为与广义相对论形式相同的部分和因Born-Infeld结构导致的复杂物质部分。
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.
Gravitational lensing in a topologically charged Eddington-inspired Born-Infeld spacetime
本文研究拓扑荷磁单极/虫洞在弱场与强场极限下的引力透镜，计算光线偏折并确定观测物理量，发现拓扑荷使观测结果区别于广义相对论虫洞情形。
In this paper we review the EiBI gravity in the presence of a cosmological constant and its tensor perturbations analysis. We show the existence of gravitational waves in the past-time, seeing as a result the smooth transition between high-energy densities (where the EBI dynamics plays its role) and low-energy densities (GR). We obtain the fluctuation spectrum for the graviton in this theory, where for small values of k the fluctuations are strongly suppressed and for large values of k these fluctuations vanish during the De Sitter expansion.
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 investigate the tensor perturbation in the inflation model driven by a massive-scalar field in Eddington-inspired Born-Infeld gravity. For short wave-length modes, the perturbation feature is very similar to that of the usual chaotic inflation. For long wave-length modes, the perturbation exhibits a peculiar rise in the power spectrum which may leave a signature in the cosmic microwave background radiation.
We study the full linear perturbations of a homogeneous and isotropic spacetime in the Eddington-inspired Born-Infeld gravity. The stability of the perturbations are analyzed in the Eddington regime. We find that, for positive $κ$, the scalar modes are stable in the infinite wavelength limit ($k=0$) but unstable for $k\neq0$. The vector modes are stable and the tensor mode is unstable in the Eddington regime, independent of the wave vector $k$. However, these modes are unstable and hence cause the instabilities for negative $κ$.
In this paper we consider an extension to Eddington's proposal for the gravitational action. We study tensor perturbations of a homogeneous and isotropic space-time in the Eddington regime, where modifications to Einstein gravity are strong. We find that the tensor mode is linearly unstable deep in the Eddington regime and discuss its cosmological implications.
We investigate the scalar perturbation produced at the pre-inflationary stage driven by a massive scalar field in Eddington-inspired Born-Infeld gravity. The scalar power spectrum exhibits a peculiar rise for low $k$-modes. The tensor-to-scalar ratio can be significantly lowered compared with that in the standard chaotic inflation model in general relativity. This result is very affirmative considering the recent dispute on the detection of the gravitational wave radiation between PLANCK and BICEP2.
We investigate the scalar perturbation of the inflation model driven by a massive-scalar field in Eddington-inspired Born-Infeld gravity. We focus on the perturbation at the attractor stage in which the first and the second slow-roll conditions are satisfied. The scalar perturbation exhibits the corrections to the chaotic inflation model in general relativity. We find that the tensor-to-scalar ratio becomes smaller than that of the usual chaotic inflation.
Eddington-inspired Born-Infeld gravity was recently proposed as an alternative to general relativity that offers a resolution of spacetime singularities. The theory differs from Einstein's gravity only inside matter due to nondynamical degrees of freedom, and it is compatible with all current observations. We show that the theory is reminiscent of Palatini f(R) gravity and that it shares the same pathologies, such as curvature singularities at the surface of polytropic stars and unacceptable Newtonian limit. This casts serious doubts on its viability.
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.
We show that electrically charged solutions within the Eddington-inspired Born-Infeld theory of gravity replace the central singularity by a wormhole supported by the electric field. As a result, the total energy associated with the electric field is finite and similar to that found in the Born-Infeld electromagnetic theory. When a certain charge-to-mass ratio is satisfied, in the lowest part of the mass and charge spectrum the event horizon disappears yielding stable remnants. We argue that quantum effects in the matter sector can lower the mass of these remnants from the Planck scale down to…
Recently, inspired by Eddington's theory, an alternative gravity called Eddington-inspired Born-Infeld gravity was proposed by Ba$\tilde{\text{n}}$ados and Ferreira. It is equivalent to Einstein's general relativity in vacuum, but deviates from it when matter is included. Interestingly, it seems that the cosmological singularities are prevented in this theory. Based on the new theory, we investigate a thick brane model with a scalar field presenting in the five-dimensional background. A domain wall solution is obtained, and further, we find that at low energy the four-dimensional Einstein grav…
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.
Within the framework of the recent Eddington-inspired Born-Infeld (EiBI) theory we study gravitational field around an $SO(3)$ global monopole. The solution also suffers from the deficit solid angle as in the Barriola-Vilenkin metric but shows a distinct feature that cannot be transformed away unless in the vanishing EiBI coupling constant, $κ$. When seen as a black hole eating up a global monopole, the corresponding Schwarzschild horizon is shrunk by $κ$. The deficit solid angle makes the space is globally not Euclidean, and to first order in $κ$ (weak-field limit) the deflection angle of lig…
We consider the Eddington-Born-Infeld (EBI) model here without assuming any cosmological constant. The EBI scalar field is supposed to play a role of both dark matter and dark energy. Different eras in cosmology are reconstructed for the model. A comparison is drawn with $Λ$CDM model using Supernova Ia, WMAP7 and BAO data. It seems that the EBI field in this form does not give good fit to observational data in comparison to the $Λ$CDM model.
In this paper we consider two different nonlinear $σ$-models minimally coupled to Eddington-inspired Born-Infeld gravity. We show that the resultant geometries represent minimal modifications with respect to those found in GR, though with important physical consequences. In particular, wormhole structures always arise, though this does not guarantee by itself the geodesic completeness of those space-times. In one of the models, quadratic in the canonical kinetic term, we identify a subset of solutions which are regular everywhere and are geodesically complete. We discuss characteristic feature…
Born-Infeld Inspired Gravity in Covariant Canonical Formalism
本文在协变正则形式下分析 Born-Infeld 启发引力，给出其 Hamiltonian 及运动方程。
We construct an axially symmetric solution of Eddington-inspired Born-Infeld gravity coupled to an electromagnetic field in 2+1 dimensions including a (negative) cosmological constant term. This is achieved by using a recently developed mapping procedure that allows to generate solutions in certain families of metric-affine gravity theories starting from a known seed solution of General Relativity, which in the present case corresponds to the electrically charged Banados-Teitelboim-Zanelli (BTZ) solution. We discuss the main features of the new configurations, including the modifications to th…
Gravitational lensing in a space-time with cosmic string within the Eddington-inspired Born-Infeld gravity
本文在EiBI引力背景时空中引入宇宙弦，推导了类光与类时测地线的有效势及光子偏转角，揭示了宇宙弦对这些物理量的修正效应。
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 investigate the evolution of the Universe filled with barotropic perfect fluid in Eddington-inspired Born-Infeld gravity. We consider both the isotropic and the anisotropic universe. At the early stage when the energy density is high, the evolution is modified considerably compared with that in general relativity. For the equation-of-state parameter $w>0$, the initial singularity is not accompanied as it was discovered for radiation in earlier work. More interestingly, for pressureless dust ($w=0$), the initial state approaches a de Sitter state. This fact opens a new possibility of singula…
The Eddington-inspired Born-Infeld (EiBI) gravity is a modification of the theory of general relativity inspired by the nonlinear Born-Infeld electrodynamics. The theory is described by a series of higher curvature terms added to the Einstein-Hilbert action with the parameter $κ$. The EiBI gravity has several interesting exact neutral and charged black hole solutions. We study the problem of overcharging extremal black hole solutions of EiBI gravity using a charged test particle to create naked singularity. We show that unlike general relativity, the overcharging could be possible for a charge…
We find an exact, rotating charged black hole solution within Eddington-inspired Born-Infeld gravity. To this end we employ a recently developed correspondence or {\it mapping} between modified gravity models built as scalars out of contractions of the metric with the Ricci tensor, and formulated in metric-affine spaces (Ricci-Based Gravity theories) and General Relativity. This way, starting from the Kerr-Newman solution, we show that this mapping bring us the axisymmetric solutions of Eddington-inspired Born-Infeld gravity coupled to a certain model of non-linear electrodynamics. We discuss …
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 study the hydrostatic equilibrium structure of compact stars in the Eddington-inspired Born-Infeld gravity recently proposed by Banados and Ferreira [Phys. Rev. Lett. 105, 011101 (2010)]. We also develop a framework to study the radial perturbations and stability of compact stars in this theory. We find that the standard results of stellar stability still hold in this theory. The frequency square of the fundamental oscillation mode vanishes for the maximum-mass stellar configuration. The dependence of the oscillation mode frequencies on the coupling parameter κof the theory is also investig…
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 $\b$.
We study the dynamics of a homogeneous and isotropic Friedmann-Robertson-Walker universe in the context of the Eddington-inspired Born-Infeld theory of gravity. We generalize earlier results, obtained in the context of a radiation dominated universe, to account for the evolution of a universe permeated by a perfect fluid with an arbitrary equation of state parameter $w$. We show that a bounce may occur for $κ>0$, if $w$ is time-dependent, and we demonstrate that it is free from tensor singularities. We argue that Eddington-inspired Born-Infeld cosmologies may be a viable alternative to the inf…
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…
We consider the scalar perturbations of Eddington-inspired Born-Infeld braneworld models in this paper. The dynamical equation for the physical propagating degree of freedom $ξ(x^μ,y)$ is achieved by using the Arnowitt-Deser-Misner decomposition method: $F_1(y) {\partial_y^2 ξ} + F_2(y){\partial_y ξ} + {\partial^μ\partial_μ}ξ=0$. We conclude that the solution is tachyonic-free and stable under scalar perturbations for $F_1(y)>0$ but unstable for $F_1(y)< 0$. The stability of a known analytic domain wall solution with the warp factor given by $a(y)= \text{sech}^{\frac{3}{4p}}(ky)$ is analyzed a…
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.
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