Charged Dilaton Black Holes Research Articles

Dilaton black holes coupled to nonlinear electrodynamic field

The theory of nonlinear electrodynamics has got a lot of attentions in recent years. It was shown that Born-Infeld nonlinear electrodynamics is not the only modification of the linear Maxwell's field which keeps the electric field of a charged point particle finite at the origin, and other type of nonlinear Lagrangian such as exponential and logarithmic nonlinear electrodynamics can play the same role. In this paper, we generalize the study on the exponential nonlinear electrodynamics by adding a scalar dilaton field to the action. By suitably choosing the coupling of the matter field to the dilaton field, we vary the action and obtain the corresponding field equations. Then, by making a proper ansatz, we construct a new class of charged dilaton black hole solutions coupled to the exponential nonlinear electrodynamics field in the presence of two Liouville-type potentials for the dilaton field. Due to the presence of the dilaton field, the asymptotic behavior of these solutions are neither flat nor (A)dS. In the limiting case where the nonlinear parameter $\beta^2$ goes to infinity, our solution reduces to the Einstein-Maxwell dilaton black holes. We obtain the mass, temperature, entropy and electric potential of these solutions. We also study the behaviour of the electric field as well as the electric potential of these black holes near the origin. We find that the electric field has a finite value \textit{near} the origin, which is the same as the electric field of Born-Infeld nonlinear electrodynamics, but it can diverge exactly at $r=0$ depending on the model parameters. We also investigate the effects of the dilaton field on the behaviour of the electric field and electric potential. Finally, we check the validity of the first law of black hole thermodynamics on the black hole horizon.

Transport Coefficients for Holographic Hydrodynamics at Finite Energy Scale

We investigate the relations between black hole thermodynamics and holographic transport coefficients in this paper. The formulae for DC conductivity and diffusion coefficient are verified for electrically single-charged black holes. We examine the correctness of the proposed expressions by taking charged dilatonic and single-charged STU black holes as two concrete examples, and compute the flows of conductivity and diffusion coefficient by solving the linear order perturbation equations. We then check the consistence by evaluating the Brown-York tensor at a finite radial position. Finally, we find that the retarded Green functions for the shear modes can be expressed easily in terms of black hole thermodynamic quantities and transport coefficients.

Remnants, fermions’ tunnelling and effects of quantum gravity

The remnants are investigated by fermions’ tunnelling from a 4-dimensional charged dilatonic black hole and a 5-dimensional black string. Based on the generalized uncertainty principle, effects of quantum gravity are taken into account. The quantum numbers of the emitted fermions affects the Hawking temperatures. For the black hole, the quantum gravity correction slows down the increase of the temperature, which leads to the remnant left in the evaporation. For the black string, the existence of the remnant is determined by the quantum gravity correction and effects of the extra compact dimension.

Charged dilatonic ads black holes and magnetic AdS D−2 × R 2 vacua

We consider D-dimensional Einstein gravity coupled to two U(1) fields and a dilaton with a scalar potential. We derive the condition that the analytical AdS black holes with two independent charges can be constructed. Turning off the cosmological constant, the extremal Reissner-Nordstrom black hole emerges as the harmonic superposition of the two U(1) building blocks. With the non-vanishing cosmological constant, our extremal solutions contain the near-horizon geometry of AdS_2 x R^{D-2} with or without a hyperscaling. We also obtain the magnetic AdS_{D-2} x Y^2 vacua where Y^2 can be R^2, S^2 or hyperbolic 2-space. These vacua arise as the fix points of some super potentials and recover the known supersymmetric vacua when the theory can be embedded in gauged supergravities. The AdS_{D-2} x R^2 vacua are of particular interest since they are dual to some quantum field theories at the lowest Landau level. By studying the embedding of some of these solutions in the string and M-theory, we find that the M2/M5-system with the equal M2 and M5 charges can intersect with another such M2/M5 on to a dyonic black hole. Analogous intersection rule applies also to the D1/D5-system. The intersections are non-supersymmetric but in the manner of harmonic superpositions.

QUASINORMAL MODES OF CHARGED DILATON BLACK HOLES AND THEIR ENTROPY SPECTRA

In this study, we employ the scalar perturbations of the charged dilaton black hole (CDBH) found by Chan, Horne and Mann (CHM), and described with an action which emerges in the low-energy limit of the string theory. A CDBH is neither asymptotically flat (AF) nor non-asymptotically flat (NAF) spacetime. Depending on the value of its dilaton parameter a, it has both Schwarzschild and linear dilaton black hole (LDBH) limits. We compute the complex frequencies of the quasinormal modes (QNMs) of the CDBH by considering small perturbations around its horizon. By using the highly damped QNM in the process prescribed by Maggiore, we obtain the quantum entropy and area spectra of these black holes (BHs). Although the QNM frequencies are tuned by a, we show that the quantum spectra do not depend on a, and they are equally spaced. On the other hand, the obtained value of undetermined dimensionless constant ϵ is the double of Bekenstein's result. The possible reason of this discrepancy is also discussed.

Subttractors

We consider extremal limits of the recently constructed "subtracted geometry". We show that extremality makes the horizon attractive against scalar perturbations, but radial evolution of such perturbations changes the asymptotics: from a conical-box to flat Minkowski. Thus these are black holes that retain their near-horizon geometry under perturbations that drastically change their asymptotics. We also show that this extremal subtracted solution ("subttractor") can arise as a boundary of the basin of attraction for flat space attractors. We demonstrate this by using a fairly minimal action (that has connections with STU model) where the equations of motion are integrable and we are able to find analytic solutions that capture the flow from the horizon to the asymptotic region. The subttractor is a boundary between two qualitatively different flows. We expect that these results have generalizations for other theories with charged dilatonic black holes.

Dynamical gap from holography in the charged dilaton black hole

We study the holographic non-relativistic fermions in the presence of the bulk dipole coupling in a charged dilatonic black hole background. We explore the nontrivial effects of the bulk dipole coupling, the fermion charge as well as the dilaton field on the flat band, the Fermi surface and the emergence of the gap by investigating the spectral function of the non-relativistic fermion system. In particular, we find that the presence of the flat band in the non-relativistic case will suppress the Fermi momentum. We also observe that the effect of the dipole coupling in the dilaton gravity is more explicit. Finally, we consider the non-relativistic fermions at nonzero temperature. A phase transition from an insulator to a conducting state is observed as the fermion system becomes hotter.

Thermodynamics and spectroscopy of charged dilaton black holes

The Bohr-Sommerfeld quantization rule is useful to study the area spectrum of black holes by employing adiabatic invariants. This method is extended to charged dilaton black holes in 2+1 dimensions. We put the background space-time into the Kruskal-like coordinate to find the period with respect to Euclidian time. Also assuming that the adiabatic invariant obeys Bohr-Sommerfeld quantization rule, detailed study of area and entropy spectrum has been done. It is dependent on the charge and is equally spaced as well. We also investigate the thermodynamics of the charged dilaton black hole.

Thermodynamics of rotating charged dilaton black holes in an external magnetic field

In the present Letter we study the long-standing problem for the thermodynamics of magnetized dilaton black holes. For this purpose we construct an exact solution describing a rotating charged dilaton black hole immersed in an external magnetic field and discuss its basic properties. We derive a Smarr-like relation and the thermodynamics first law for these magnetized black holes. The novelty in the thermodynamics of the magnetized black holes is the appearance of new terms proportional to the magnetic momentum of the black holes in the Smarr-like relation and the first law.

Electrically charged dilaton black holes in an external magnetic field

In the present paper, we construct a new solution to the Einstein-Maxwell-dilaton gravity equations describing electrically charged dilaton black holes immersed in a strong external magnetic field, and we study its properties. The black holes described by the solution are rotating but with zero total angular momentum and possess an ergoregion confined in a neighborhood of the horizon. Our results also show that the external magnetic field does not affect the black hole thermodynamics.

DIPOLE COUPLING EFFECT OF HOLOGRAPHIC FERMION IN CHARGED DILATONIC GRAVITY

In this note, we study the dipole coupling effect of holographic fermion in a charged dilatonic black hole proposed by Gubser and Rocha.1 It is found that the property of Fermi liquid is rigid under perturbation of dipole coupling, and the Fermi momentum is linearly shifted. A gap is dynamically generated as the coupling becomes large enough and the Fermi surface ceases to exist as the bulk dipole coupling further increases.

Legendre Invariance and Geometrothermodynamics Description of the 3D Charged-Dilaton Black Hole

We first review Weinhold information geometry and Ruppeiner information geometry of 3D charged-dilaton black hole. Then, we use the Legendre invariant to introduce a 2-dimensional thermodynamic metric in the space of equilibrium states, which becomes singular at those points. According to the analysis of the heat capacities, these points are the places where phase transitions occur. This result is valid for the black hole, therefore, provides a geometrothermodynamics description of black hole phase transitions in terms of curvature singularities.

Thermal properties of charged dilaton black hole, energy and momentum in teleparallel equivalent of general relativity

Two different charged dilaton black holes in 4-dimension, within teleparallel equivalent of general relativity (TEGR), are derived. These solutions are related through local Lorentz transformation. The total energy of these black holes, using three different methods, the Hamiltonian method, the translational momentum 2-form and the Euclidean continuation method given by Gibbons and Hawking, is calculated. It is shown that the three methods give the same results. The value of energy is shown to depend on the mass M and charge q. The verification of the first law of thermodynamics is proved. Finally, it is shown that if the charge q is vanishing then, the total energy reduced to that of Schwarzschild’s black hole.

On holographic entanglement entropy of charged matter

We study holographic entanglement entropy in the background of charged dilatonic black holes which can be viewed as holographic duals of certain finite density states of N=4 super Yang-Mills. These charged black holes are distinguished in that they have vanishing ground state entropy. The entanglement entropy for a slab experiences a second order phase transition as the thickness of the slab is varied, while the entanglement entropy for a sphere is a smooth function of the radius. This suggests that the second scale introduced by the anisotropy of the slab plays an important role in driving the phase transition. In both cases we do not observe any logarithmic violation of the area law indicative of hidden Fermi surfaces. We investigate how these results are affected by the inclusion of the Gauss-Bonnet term in the bulk gravitational action. We also observe that such addition to the bulk action does not change the logarithmic violation of the area law in the backgrounds with hyperscaling violation.

Scalar field radiation from dilatonic black holes

We study radiation of scalar particles from charged dilaton black holes. The Hamilton–Jacobi method has been used to work out the tunneling probability of outgoing particles from the event horizon of dilaton black holes. For this purpose we use WKB approximation to solve the charged Klein–Gordon equation. The procedure gives Hawking temperature for these black holes as well.

Stringy stability of charged dilaton black holes with flat event horizon

Abstract Electrically charged black holes with flat event horizon in anti-de Sitter space have received much attention due to various applications in Anti-de Sitter/Conformal Field Theory (AdS/CFT) correspondence, from modeling the behavior of quark-gluon plasma to superconductor. Crucial to the physics on the dual field theory is the fact that when embedded in string theory, black holes in the bulk may become vulnerable to instability caused by brane pair-production. Since dilaton arises naturally in the context of string theory, we study the effect of coupling dilaton to Maxwell field on the stability of flat charged AdS black holes. In particular, we study the stability of Gao-Zhang black holes, which are locally asymptotically anti-de Sitter. We find that for dilaton coupling parameter α > 1, flat black holes are stable against brane pair production, however for 0 ≤ α < 1, the black holes eventually become unstable as the amount of electrical charges is increased. Such instability however, behaves somewhat differently from that of flat Reissner-Nordström black holes. In addition, we prove that the Seiberg-Witten action of charged dilaton AdS black hole of Gao-Zhang type with flat event horizon (at least in 5-dimension) is always logarithmically divergent at infinity for finite values of α, and is finite and positive in the case α → ∞. We also comment on the robustness of our result for other charged dilaton black holes that are not of Gao-Zhang type.

Dipole coupling effect of holographic fermion in charged dilatonic gravity

In this Letter, we study the dipole coupling effect of holographic fermion in a charged dilatonic black hole proposed by Gubser and Rocha (2010) [1]. It is found that the property of Fermi liquid is rigid under perturbation of dipole coupling, and the Fermi momentum is linearly shifted. A gap is dynamically generated as the coupling becomes large enough and the Fermi surface ceases to exist as the bulk dipole coupling further increases.

Effect of the cosmological constant in the Hawking radiation of 3D charged dilaton black hole

This paper deals with the semiclassical radiation spectrum of static and circularly symmetric 3D charged dilaton black holes with cosmological constant {\Lambda} in non-asymptotically flat spacetimes. We first review the 3D charged dilaton black holes which are solution to low-energy string action. The wave equation of a massless scalar field is shown to be exactly solvable in terms of hypergeometric functions. Thus, the radiation spectrum and its corresponding temperature are obtained, precisely. Computations at high frequency regime show that the radiation spectrum yields the Hawking temperature of the black hole with no charge. Unlike the chargeless case, the Hawking temperature of the charged dilaton black holes is derived from the radiation spectrum at the low frequencies. The utmost importance of the {\Lambda} in the latter result is highlighted.

Holographic non-relativistic fermionic fixed point by the charged dilatonic black hole

Driven by the landscape of garden-variety condensed matter systems, we have investigated how the dual spectral function behaves at the non-relativistic as well as relativistic fermionic fixed point by considering the probe Dirac fermion in an extremal charged dilatonic black hole with zero entropy. Although the pattern for both of the appearance of flat band and emergence of Fermi surface is qualitatively similar to that given by the probe fermion in the extremal Reissner-Nordstrom AdS black hole, we find a distinctly different low energy behavior around the Fermi surface, which can be traced back to the different near horizon geometry. In particular, with the peculiar near horizon geometry of our extremal charged dilatonic black hole, the low energy behavior exhibits the universal linear dispersion relation and scaling property, where the former indicates that the dual liquid is a Fermi one while the latter implies that the dual liquid is not exactly of Landau Fermi type.

Some properties of the holographic fermions in an extremal charged dilatonic black hole

We study the properties of the Green's functions of the fermions in the extremal charged dilatonic black hole proposed by Gubser and Rocha [Phys. Rev. D \textbf{81}, 046001 (2010)]. We find that many properties seem to be in agreement with that of Fermi liquid. Especially, the dispersion relation is linear. It is very different from that found in the extremal Reissner-Nordstr$\ddot{o}$m (RN) black hole for massless fermion, which is obviously non-Fermi liquid due to a nonlinear dispersion relation. However, for another scaling behavior of the height of $ImG_{11}$ at the maximum, the scaling exponent is not one, which is at odds with that found in the RN black hole.