Holographic superconductors in the Born–Infeld electrodynamics

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 mean that it is harder for the scalar condensation to form in the Born–Infeld electrodynamics.     

Domain wall universe in the Einstein–Born–Infeld theory

In this Letter, we discuss the dynamics of a domain wall universe embedded into the charged black hole spacetime of the Einstein–Born–Infeld (EBI) theory. There are four kinds of possible spacetime structures, i.e., those with no horizon, the extremal one, those with two horizons (as the Reissner–Nordström black hole), and those with a single horizon (as the Schwarzshild black hole). We derive the effective cosmological equations on the wall. In contrast to the previous works, we take the contribution of the electrostatic energy on the wall into account. By examining the properties of the effective potential, we find that a bounce can always happen outside the (outer) horizon. For larger masses of the black hole, the height of the barrier between the horizon and bouncing point in the effective potential becomes smaller, leading to longer time scales of bouncing process. These results are compared with those in the previous works.     

Hawking radiation received at infinity in higher dimensional Reissner-Nordstr?m black hole spacetimes

In this study, we investigate the Hawking radiation in higher dimensional Reissner-Nordstr?m black holes as received by an observer located at infinity. The frequency-dependent transmission rates, which deform the thermal radiation emitted in the vicinity of the black hole horizon, are evaluated numerically. In addition to those in four-dimensional spacetime, the calculations are extended to higher dimensional Reissner-Nordstr?m metrics, and the results are observed to be sensitive to the spacetime dimension to an extent. Generally, we observe that the transmission coefficient practically vanishes when the frequency of the emitted particle approaches zero. It increases with frequency and eventually saturates to a certain value. For four-dimensional spacetime, the above result is demonstrated to be mostly independent of the metric's parameter and the orbital quantum number of the particle, when the location of the event horizon, \begin{document}$ r_h$\end{document}, and the product of the charges of the black hole and the particle qQ are known. However, for higher-dimensional scenarios, the convergence becomes more gradual. Moreover, the difference between states with different orbital quantum numbers is observed to be more significant. As the magnitude of the product of charges qQ becomes more significant, the transmission coefficient exceeds 1. In other words, the resultant spectral flux is amplified, which results in an accelerated process of black hole evaporation. The relationship of the calculated outgoing transmission coefficient with existing results on the greybody factor is discussed.     

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

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

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.     

Wormhole solutions in Gauss–Bonnet–Born–Infeld gravity

A new class of solutions which yields an (n + 1)-dimensional spacetime with a longitudinal nonlinear magnetic field is introduced. These spacetimes have no curvature singularity and no horizon, and the magnetic field is non singular in the whole spacetime. They may be interpreted as traversable wormholes which could be supported by matter not violating the weak energy conditions. We generalize this class of solutions to the case of rotating solutions and show that the rotating wormhole solutions have a net electric charge which is proportional to the magnitude of the rotation parameter, while the static wormhole has no net electric charge. Finally, we use the counterterm method and compute the conserved quantities of these spacetimes.     

Quantum anomaly at horizon and Hawking radiation from higher dimensional Reissner–Nordström–de Sitter black hole

Based on the anomaly cancellation method, initiated by Robinson and Wilczek, we investigate Hawking radiation from the event horizon and cosmological horizon of the higher dimensional Reissner–Nordström–de Sitter black hole via covariant gauge and gravitational anomalies. Unlike in black hole space-time, to describe the observable physics, the effective field theory here is constructed between the event horizon and cosmological horizon. Our result shows that to restore the underlying gauge covariance and diffeomorphism covariance at the quantum level, the covariant compensating fluxes of gauge and energy–momentum tensor, which are shown to equal to those of Hawking radiation, should be radiated from the event horizon and absorbed from the cosmological horizon, respectively.     

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.     

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.     

Exact solutions of the Klein–Gordon equation in the Kerr–Newman background and Hawking radiation

This work considers the influence of the gravitational field produced by a charged and rotating black hole (Kerr–Newman spacetime) on a charged massive scalar field. We obtain exact solutions of both angular and radial parts of the Klein–Gordon equation in this spacetime, which are given in terms of the confluent Heun functions. From the radial solution, we obtain the exact wave solutions near the exterior horizon of the black hole, and discuss the Hawking radiation of charged massive scalar particles.     

Thoughts on entropic gravity in the Parikh–Wilczek tunneling model of Hawking radiation

In this letter, we use the Parikh–Wilczek tunneling model of Hawking radiation to illustrate that a reformulation of Verlinde’s entropic gravity is needed to derive Newton’s law for a temperature-varying screen, required by the conservation of energy. Furthermore, the entropy stored in the holographic screen is shown to be additive and its temperature dependence can be obtained.     

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.     

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.     

The geometry of the higher dimensional black hole thermodynamics in Einstein–Gauss–Bonnet theory

In this paper, we have studied the geometry of the five-dimensional black hole solutions in (a) Einstein–Yang–Mills–Gauss–Bonnet theory and (b) Einstein–Maxwell–Gauss–Bonnet theory with a cosmological constant for spherically symmetric space time. Formulating the Ruppeiner metric, we have examined the possible phase transition for both the metrics. It is found that depending on some restrictions phase transition is possible for the black holes. Also for Λ = 0 in Einstein–Gauss–Bonnet black hole, the Ruppeiner metric becomes flat and hence the black hole becomes a stable one.