Liouville-type Dilaton Potentials Research Articles

A new black hole solution in dilaton gravity inspired by power-law electrodynamics

In this work, a new class of slowly rotating black hole solutions in dilaton gravity has been obtained where dilaton field is coupled with nonlinear Maxwell invariant. The background space–time is a stationary axisymmetric geometry. Here, it has been shown that the dilaton potential can be written in the form of generalized three Liouville-type potentials. In the presence of these three Liouville-type dilaton potentials, the asymptotic behavior of the obtained solutions is neither flat nor (A)dS. One bizarre property of the electric field is that the electric field goes to zero when [Formula: see text] and diverges at [Formula: see text]. We show the validity of the first law of thermodynamics in thermodynamic investigations. The local and global thermodynamical stability are investigated through the use of heat capacity and Gibbs free energy. Also, the bounded, phase transition and the Hawking–Page phase transition points as well as the ranges of black hole stability have been shown in the corresponding diagrams. From these diagrams, we can say that the presence of the dilaton field makes the solutions to be locally stable near origin and vanishes the global stability of our solutions. In final thermodynamics analysis, we obtain the Smarr formula for our solution. We will show that the presence of dilaton field brings a new term in the Smarr formula. Also, we find that the dilaton field makes the black hole (AdS) mass to decrease for every fix values of [Formula: see text] (entropy).

Asymptotically (A)dS dilaton black holes with nonlinear electrodynamics

It is well known that with an appropriate combination of three Liouville-type dilaton potentials, one can construct charged dilaton black holes in an (anti)-de Sitter [(A)dS] spaces in the presence of linear Maxwell field. However, asymptotically (A)dS dilaton black holes coupled to nonlinear gauge field have not been found. In this paper, we construct, for the first time, three new classes of dilaton black hole solutions in the presence of three types of nonlinear electrodynamics, namely Born–Infeld (BI), Logarithmic (LN) and Exponential nonlinear (EN) electrodynamics. All these solutions are asymptotically (A)dS and in the linear regime reduce to the Einstein–Maxwell-dilaton (EMd) black holes in (A)dS spaces. We investigate physical properties and the causal structure, as well as asymptotic behavior of the obtained solutions, and show that depending on the values of the metric parameters, the singularity can be covered by various horizons. We also calculate conserved and thermodynamic quantities of the obtained solutions. Interestingly enough, we find that the coupling of dilaton field and nonlinear gauge field in the background of (A)dS spaces leads to a strange behavior for the electric field. We observe that the electric field is zero at singularity and increases smoothly until reaches a maximum value, then it decreases smoothly until goes to zero as [Formula: see text]. The maximum value of the electric field increases with increasing the nonlinear parameter [Formula: see text] or decreasing the dilaton coupling [Formula: see text] and is shifted to the singularity in the absence of either dilaton field ([Formula: see text]) or nonlinear gauge field ([Formula: see text]).

Thermodynamic geometry of charged dilaton black holes in AdS spaces

It was shown that with the combination of three Liouville-type dilaton potentials, one can derive dilaton black holes in the background of anti-de-Sitter (AdS) spaces. In this paper, we further extend the study on the dilaton AdS black holes by investigating their thermodynamic instability through a geometry approach. First, we review thermodynamic quantities of the solutions and check the validity of the first law of thermodynamics. Then, we investigate phase transitions and stability of the solutions. In particular, we disclose the effects of the dilaton field on the stability of the black holes. We also employ the geometrical approach toward thermodynamical behavior of the system and find that the divergencies in the Ricci scalar coincide with roots and divergencies in the heat capacity. We find that the behavior of the Ricci scalar around divergence points depends on the type of the phase transition.

Thermodynamics of rotating black branes in higher dimensional Einstein – nonlinear electrodynamics – dilaton gravity

In this paper, we propose a n-dimensional action in which gravity is coupled to exponential nonlinear electrodynamics and scalar dilaton field with Liouville-type potential. By varying the action, we obtain the field equations. Then, we construct a new class of charged, rotating black brane solutions, with k = [(n – 1)/2] rotation parameters, of this theory. Because of the presence of the Liouville-type dilaton potential, the asymptotic behavior of the obtained solutions is neither flat nor (anti)-de Sitter. We investigate the causal structure of the space–time in ample details. We find the suitable counter term that removes the divergences of the action in the presence of the dilaton field, and calculate the conserved and thermodynamic quantities of the space–time. Interestingly enough, we find that the conserved quantities crucially depend on the dilaton coupling constant, α, while they are independent of the nonlinear parameter, β. We also check the validity of the first law of thermodynamics on the black brane horizon. Finally, we study thermal stability of the solutions by computing the heat capacity in the canonical ensemble. We disclose the effects of rotation parameter, nonlinearity of electrodynamics, and dilaton field on the thermal stability conditions.

Thermodynamic geometry and thermal stability ofn-dimensional dilaton black holes in the presence of logarithmic nonlinear electrodynamics

In this paper, we construct a new class of black hole solutions which is coupled to the logarithmic nonlinear electrodynamics in the context of dilaton gravity. We consider an $n$-dimensional action in which gravity is coupled to the logarithmic nonlinear electrodynamics field and a scalar dilaton field to obtain the equations of motion of the gravitational, dilaton and electromagnetic fields. This leads to finding a new class of $n$-dimensional static and spherically symmetric black hole solutions in the presence of two Liouville-type dilaton potentials. The asymptotic behavior of these solutions is neither flat nor (anti-)de Sitter [(A)dS], and in the limiting case where the nonlinear parameter $\ensuremath{\beta}$ goes to infinity, our solutions reduce to the black holes of Einstein-Maxwell-dilaton gravity in higher dimensions. Thermodynamic quantities such as mass, temperature, electric potential and entropy are also computed, and it is shown that they agree with the first law of thermodynamics. Furthermore, we find that for small values of the electric charge parameter $q$, and the dilaton coupling constant $\ensuremath{\alpha}$, as well as small dimension $n$, the solutions are thermally stable. By increasing $n$, the region of stability stands for smaller values of $\ensuremath{\alpha}$ independent of $q$. Finally, we use the method of thermodynamical geometry and find the phase transition points by calculating the Ricci scalar of a thermodynamic metric.

Phase transition and thermodynamic geometry of topological dilaton black holes in gravitating logarithmic nonlinear electrodynamics

Considering the Lagrangian of the logarithmic nonlinear electrodynamics in the presence of a scalar dilaton field, we obtain a new class of topological black hole solutions of Einstein-dilaton gravity with two Liouville-type dilaton potentials. Black hole horizons and cosmological horizons, in these spacetimes, can be a two-dimensional positive, zero, or negative constant curvature surface. We find that the behavior of the electric field crucially depends on the dilaton coupling constant $\ensuremath{\alpha}$. For small $\ensuremath{\alpha}$, the electric field diverges near the origin, although its divergency is weaker than the linear Maxwell field. However, with increasing $\ensuremath{\alpha}$, the behavior of the electric field, near the origin, approaches to that of the Maxwell field. We also study casual structure, asymptotic behavior, and physical properties of the solutions. We find that, depending on the model parameters, the topological dilaton black holes may have one or two horizons, and even in some cases we encounter a naked singularity without horizon. We compute the conserved and thermodynamic quantities of the spacetime and investigate that these quantities satisfy the first law of thermodynamics. We also probe thermal stability in the canonical and grand canonical ensembles and disclose the effects of the dilaton field as well as nonlinear parameter on the thermal stability of the solutions. Finally, we investigate thermodynamical geometry of the obtained solutions by introducing a new metric and studying the phase transition points due to the divergency of the Ricci scalar. We find that the dilaton field affects the phase transition points of the system.

Higher dimensional dilaton black holes in the presence of exponential nonlinear electrodynamics

We examine the higher dimensional action in which gravity is coupled to the exponential nonlinear electrodynamic and a scalar dilaton field. We construct a new class of $n$-dimensional static and spherically symmetric black hole solutions of this theory in the presence of the dilaton potential with two Liouville-type terms. In the presence of two Liouville-type dilaton potential, the asymptotic behavior of the obtained black holes are neither flat nor (A)dS. Due to the nonlinear nature of electrodynamic field, the electric field has finite value near the origin where $r\rightarrow0$ and goes to zero as $r\rightarrow\infty$. Interestingly enough, we find that in the absence of the dilaton field, the electric field has a finite value at $r=0$, while as soon as the dilaton field is taken into account, the electric field diverges as $r\rightarrow 0$. This implies that the presence of the dilaton field changes the behaviour of the electric field near the origin. In the limiting case where the nonlinear parameter $\beta$ goes to infinity, our solutions reduce to dilaton black holes of Einstein-Maxwell-dilaton gravity in higher dimensions. We compute the conserved and thermodynamic quantities of the solutions and show that these quantities satisfy the first law of black holes thermodynamics on the horizon.

Transport in non-conformal holographic fluids

We have considered non-conformal fluid dynamics whose gravity dual is a certain Einstein dilaton system with Liouville type dilaton potential, characterized by an intrinsic parameter $\eta$. We have discussed the Hawking-Page transition in this framework using hard-wall model and it turns out that the critical temperature of the Hawking-Page transition encapsulates a non-trivial dependence on $\eta$. We also obtained transport coefficients such as AC conductivity, shear viscosity and diffusion constant in the hydrodynamic limit, which show non-trivial $\eta$ dependent deviations from those in conformal fluids, although the ratio of the shear viscosity to entropy density is found to saturate the universal bound. Some of the retarded correlators are also computed in the high frequency limit for case study.

Magnetic dilaton strings in anti-de Sitter spaces

With an appropriate combination of three Liouville-type dilaton potentials, we construct a new class of spinning magnetic dilaton string solutions which produces a longitudinal magnetic field in the background of anti-de Sitter spacetime. These solutions have no curvature singularity and no horizon, but have a conic geometry. We find that the spinning string has a net electric charge which is proportional to the rotation parameter. We present the suitable counterterm which removes the divergences of the action in the presence of dilaton potential. We also calculate the conserved quantities of the solutions by using the counterterm method.

THERMODYNAMICAL PROPERTIES OF TOPOLOGICAL BORN–INFELD-DILATON BLACK HOLES

We examine the (n + 1)-dimensional (n ≥ 3) action in which gravity is coupled to the Born–Infeld nonlinear electrodynamic and a dilaton field. We construct a new (n + 1)-dimensional analytic solution of this theory in the presence of Liouville-type dilaton potentials. These solutions, which describe charged topological dilaton black holes with nonlinear electrodynamics, have unusual asymptotics. They are neither asymptotically flat nor (anti)-de Sitter. The event horizons of these black holes can be an (n - 1)-dimensional positive, zero or negative constant curvature hypersurface. We also analyze the thermodynamics and stability of these solutions and disclose the effect of the dilaton and Born–Infeld fields on the thermal stability in the canonical ensemble.

Higher dimensional slowly rotating dilaton black holes in AdS spacetime

In this paper, with an appropriate combination of three Liouville-type dilaton potentials, we obtain the higher dimensional charged slowly rotating dilaton black hole solution for asymptotically anti-de Sitter spacetime. The angular momentum and the gyromagnetic ratio of such a black hole are determined for the arbitrary values of the dilaton coupling constant. It is shown that the dilaton field modifies the gyromagnetic ratio of the rotating dilaton black holes.

Charged rotating dilaton black strings in (A)dS spaces

We derive a class of charged rotating dilaton black string solutions in the background of anti-de Sitter spaces with an appropriate combination of three Liouville-type dilaton potentials. We also present the suitable counterterm which removes the divergences of the action in the presence of dilaton potential. The solutions are analyzed and their thermodynamics are discussed by using the counterterm method.

Slowly rotating dilaton black hole in anti–de Sitter spacetime

A rotating dilaton black hole solution for asymptotically anti-de Sitter spacetime is obtained in the small angular momentum limit with an appropriate combination of three Liouville-type dilaton potentials. The angular momentum, magnetic dipole moment, and the gyromagnetic ratio of such a black hole are determined for arbitrary values of the dilaton-electromagnetic coupling parameter.

Dilaton black holes in the de Sitter or anti–de Sitter universe

Poletti and Wiltshire have shown that, with the exception of a pure cosmological constant, the solution of a dilaton black hole in the background of de Sitter or anti-de Sitter universe, does not exist in the presence of one Liouville-type dilaton potential. Here with the combination of three Liouville-type dilaton potentials, we obtain the dilaton black hole solutions in the background of de Sitter or anti-de Sitter universe.

Nonasymptotically AdS/dS solutions and their higher dimensional origins

We look for and analyze in some details some exact solutions of Einstein-Maxwell-dilaton gravity with one or two Liouville-type dilaton potential(s) in an arbitrary dimension. Such a theory could be obtained by dimensionally reducing Einstein-Maxwell theory with a cosmological constant to a lower dimension. These (neutral/magnetic/electric charged) solutions can have a (two) black hole horizon(s), cosmological horizon, or a naked singularity. Black hole horizon or cosmological horizon of these solutions can be a hypersurface of positive, zero or negative constant curvature. These exact solutions are neither asymptotically flat, nor asymptotically AdS/dS. But some of them can be uplifted to a higher dimension, and those higher dimensional solutions are either asymptotically flat, or asymptotically AdS/dS with/without a compact constant curvature space. This observation is useful to better understand holographic properties of these non-asymptotically AdS/dS solutions.

Melvin solution with a dilaton potential

We find new Melvin-like solutions in Einstein–Maxwell–dilaton gravity with a Liouville-type dilaton potential. The properties of the corresponding solution in Freedman–Schwarz gauged supergravity model are extensively studied. We show that this configuration is regular and geodesically complete but does not preserve any supersymmetry. An exact solution describing travelling waves in this Melvin-type background is also presented.

Holography and brane cosmology in domain wall backgrounds

We consider a class of domain-wall black hole solutions in dilaton gravity with a Liouville-type dilaton potential. Using the surface counterterm approach we calculate the stress-energy tensor of quantum field theory (QFT) corresponding to the domain-wall black hole in the domain-wall--QFT correspondence. A brane universe is investigated in the domain-wall black hole background. When the tension term of the brane is equal to the surface counterterm, we find that the equation of motion of the brane can be mapped to the standard form of Friedmann-Robertson-Walker equations, but with a varying gravitational constant on the brane. A Cardy-Verlinde-like formula is found, which relates the entropy density of the QFT to its energy density. At the moment when the brane crosses the black hole horizon of the background, the Cardy-Verlinde-like formula coincides with the Friedmann equation of the brane universe, and the Hubble entropy bound is saturated by the entropy of domain-wall black holes.

Topological dilaton black holes

In four-dimensional spacetime, when the two-sphere of black hole event horizons is replaced by a two-dimensional hypersurface with zero or negative constant curvature, the black hole is referred to as a topological black hole. In this paper we present some exact topological black hole solutions in the Einstein-Maxwell dilaton theory with a Liouville-type dilaton potential.

Black plane solutions in four-dimensional spacetimes.

The static, plane symmetric solutions and cylindrically symmetric solutions of Einstein-Maxwell equations with a negative cosmological constant are investigated. These black configurations are asymptotically anti-de Sitter not only in the transverse directions, but also in the membrane or string directions. Their causal structure is similar to that of Reissner-Nordstr\"{o}m black holes, but their Hawking temperature goes with $M^{1/3}$, where $M$ is the ADM mass density. We also discuss the static plane solutions in Einstein-Maxwell-dilaton gravity with a Liouville-type dilaton potential. The presence of the dilaton field changes drastically the structure of solutions. They are asymptotically ``anti-de Sitter'' or ``de Sitter'' depending on the parameters in the theory.