A self-gravitating Dirac–Born–Infeld global monopole

We generalize the field theory of the global monopole to the Dirac–Born–Infeld (DBI) field and investigate the gravitational property of a DBI global monopole in four-dimensional spherically symmetric spacetime. The coupled equations for the metric and the DBI scalar field are solved asymptotically and numerically. It is found that, just as for a canonical global monopole, the gravitational effect of the DBI global monopole is equivalent to that of a deficit solid angle in the metric plus a negative mass at the origin. However, compared with a canonical global monopole, for the same false vacuum and symmetry-breaking scale, a DBI global monopole has a relatively smaller core and a larger absolute value of effective mass. Thus, it can yield a larger deflect angle when the light is passing by. Especially, when the scale of the warp factor is small enough, the effective mass of a DBI global monopole does not depend apparently on the value of the false vacuum, which is qualitatively different from that of a canonical global monopole.     

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$q$ 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$q$, the dilaton coupling constant, α$\alpha$, and the Born–Infeld parameter, β$\beta$, modify the Smarr formula and the values of the gyromagnetic ratio of the extremal charged rotating black holes.     

Geonic black holes and remnants in Eddington-inspired Born–Infeld gravity

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 the TeV scale.     

Topological Born–Infeld-dilaton black holes

We construct a new analytic solution of Einstein–Born–Infeld-dilaton theory in the presence of Liouville-type potentials for the dilaton field. These solutions describe dilaton black holes with nontrivial topology and nonlinear electrodynamics. Black hole horizons and cosmological horizons in these spacetimes, can be a two-dimensional positive, zero or negative constant curvature surface. The asymptotic behavior of these solutions are neither flat nor (A)dS. We calculate the conserved and thermodynamic quantities of these solutions and verify that these quantities satisfy the first law of black hole thermodynamics.     

N-dimensional non-abelian dilatonic,stable black holes and their Born–Infeld extension

We find large classes of non-asymptotically flat Einstein–Yang–Mills–Dilaton and Einstein–Yang–Mills–Born–Infeld–Dilaton black holes in N-dimensional spherically symmetric spacetime expressed in terms of the quasilocal mass. Extension of the dilatonic YM solution to N-dimensions has been possible by employing the generalized Wu-Yang ansatz. Another metric ansatz, which aided in finding exact solutions is the functional dependence of the radius function on the dilaton field. These classes of black holes are stable against linear radial perturbations. In the limit of vanishing dilaton we obtain Bertotti–Robinson type metrics with the topology of AdS ₂×S ^N–2. Since connection can be established between dilaton and a scalar field of Brans–Dicke type we obtain black hole solutions also in the Brans–Dicke–Yang–Mills theory as well.     

P–V criticality of topological black holes in Lovelock–Born–Infeld gravity

To understand the effect of third order Lovelock gravity, $P$ – $V$ criticality of topological AdS black holes in Lovelock–Born–Infeld gravity is investigated. The thermodynamics is further explored with some more extensions and in some more detail than the previous literature. A detailed analysis of the limit case $\beta \rightarrow \infty $ is performed for the seven-dimensional black holes. It is shown that, for the spherical topology, $P$ – $V$ criticality exists for both the uncharged and the charged cases. Our results demonstrate again that the charge is not the indispensable condition of $P$ – $V$ criticality. It may be attributed to the effect of higher derivative terms of the curvature because similar phenomenon was also found for Gauss–Bonnet black holes. For $k=0$ , there would be no $P$ – $V$ criticality. Interesting findings occur in the case $k=-1$ , in which positive solutions of critical points are found for both the uncharged and the charged cases. However, the $P$ – $v$ diagram is quite strange. To check whether these findings are physical, we give the analysis on the non-negative definiteness condition of the entropy. It is shown that, for any nontrivial value of $\alpha $ , the entropy is always positive for any specific volume $v$ . Since no $P$ – $V$ criticality exists for $k=-1$ in Einstein gravity and Gauss–Bonnet gravity, we can relate our findings with the peculiar property of third order Lovelock gravity. The entropy in third order Lovelock gravity consists of extra terms which are absent in the Gauss–Bonnet black holes, which makes the critical points satisfy the constraint of non-negative definiteness condition of the entropy. We also check the Gibbs free energy graph and “swallow tail” behavior can be observed. Moreover, the effect of nonlinear electrodynamics is also included in our research.     

Gravitational perturbation and quasi-normal modes of charged black holes in Einstein–Born–Infeld gravity

Born–Infeld electrodynamics has attracted considerable interest due to its relation to strings and D-branes. In this paper the gravitational perturbations of electrically charged black holes in Einstein–Born–Infeld gravity are studied. The effective potentials for axial perturbations are derived and discussed. The quasi normal modes for the gravitational perturbations are computed using a WKB method. The modes are compared with those of the Reissner–Nordström black hole. The relation of the quasi normal modes with the non-linear parameter and the spherical index are also investigated. Comments on stability of the black hole and on future directions are madeThis revised version was published online in April 2005. The publishing date was inserted.     

Varying alpha driven by the Dirac–Born–Infeld scalar field

Since about ten years ago, varying α theories attracted many attentions, mainly due to the first observational evidence from the quasar absorption spectra that the fine structure “constant” might change with cosmological time. In this Letter, we investigate the cosmic evolution of α   driven by the Dirac–Born–Infeld (DBI) scalar field. To be general, we consider various couplings between the DBI scalar field and the electromagnetic field. We also confront the resulting Δα/α$\mathrm{\Delta }\alpha /\alpha$ with the observational constraints, and find that various cosmological evolution histories of Δα/α$\mathrm{\Delta }\alpha /\alpha$ are allowed. Comparing with the case of varying α driven by quintessence, the corresponding constraints on the parameters of coupling have been relaxed, thanks to the relativistic correction of the DBI scalar field.     

The Born–Infeld sphaleron

We study the SU(2) electroweak model in which the standard Yang–Mills coupling is supplemented by a Born–Infeld term. The deformation of the sphaleron and bisphaleron solutions due to the Born–Infeld term is investigated and new branches of solutions are exhibited. Especially, we find a new branch of solutions connecting the Born–Infeld sphaleron to the first solution of the Kerner–Gal'tsov series.     

General holographic superconductor models with Born–Infeld electrodynamics

A general class of holographic superconductor models in Schwarzschild AdS black hole with the Born–Infeld electrodynamics is investigated. It is found that the Born–Infeld coupling parameter affects the critical temperature, the order of phase transitions, the conductivity and the critical exponents near the second-order phase transition point. It is also noted that both the position of the conductivity coherence peak and the ratio of the gap frequency in conductivity to the critical temperature depend on the model parameters and the Born–Infeld coupling parameter.     

Thermodynamics,phase transitions and Ruppeiner geometry for Einstein–dilaton–Lifshitz black holes in the presence of Maxwell and Born–Infeld electrodynamics

In this paper, we first obtain the higher-dimen-sional dilaton–Lifshitz black hole solutions in the presence of Born–Infeld (BI) electrodynamics. We find that there are two different solutions for the cases of \(z=n+1\) and \(z\ne n+1\) where z is the dynamical critical exponent and n is the number of spatial dimensions. Calculating the conserved and thermodynamical quantities, we show that the first law of thermodynamics is satisfied for both cases. Then we turn to the study of different phase transitions for our Lifshitz black holes. We start with the Hawking–Page phase transition and explore the effects of different parameters of our model on it for both linearly and BI charged cases. After that, we discuss the phase transitions inside the black holes. We present the improved Davies quantities and prove that the phase transition points shown by them are coincident with the Ruppeiner ones. We show that the zero temperature phase transitions are transitions in the radiance properties of black holes by using the Landau–Lifshitz theory of thermodynamic fluctuations. Next, we turn to the study of the Ruppeiner geometry (thermodynamic geometry) for our solutions. We investigate thermal stability, interaction type of possible black hole molecules and phase transitions of our solutions for linearly and BI charged cases separately. For the linearly charged case, we show that there are no phase transitions at finite temperature for the case \( z\ge 2\). For \(z<2\), it is found that the number of finite temperature phase transition points depends on the value of the black hole charge and there are not more than two. When we have two finite temperature phase transition points, there is no thermally stable black hole between these two points and we have discontinuous small/large black hole phase transitions. As expected, for small black holes, we observe finite magnitude for the Ruppeiner invariant, which shows the finite correlation between possible black hole molecules, while for large black holes, the correlation is very small. Finally, we study the Ruppeiner geometry and thermal stability of BI charged Lifshtiz black holes for different values of z. We observe that small black holes are thermally unstable in some situations. Also, the behavior of the correlation between possible black hole molecules for large black holes is the same as for the linearly charged case. In both the linearly and the BI charged cases, for some choices of the parameters, the black hole system behaves like a Van der Waals gas near the transition point.